Perpendicular Bisectors Geometry Special Properties and Parts of Triangles Perpendicular Bisectors Questions What is a perpendicular bisector? What is the difference between medians, perpendicular bisectors, and altitudes? What is an example of a real world situation that implies the perpendicular bisector theorem? How do you find the perpendicular bisectors of a triangle? How do you write the equation of the perpendicular bisector of the segment with the given endpoints (2,5) and (4,9)? How do you find the equation for the perpendicular bisector of the segment with endpoints (-1,-3) and (7,1)? How do I find the equation of a perpendicular bisector of a line segment with the endpoints (-2, -4) and (6, 4)? What is the difference between a bisector and a perpendicular bisector? Given point A (-2,1) and point B (1,3), how do you find the equation of the line perpendicular to the line AB at its midpoint? How do I write an equation for the perpendicular bisector of the segment joining the points (5,-4) and (-3,-2)? What is the equation of the perpendicular bisector of a chord of a circle? What is the perpendicular bisector of a line with points at A (-33, 7.5) and B (4,17)? How do you find the equation of the perpendicular bisector of the points (1,4) and (5,-2)? How do you find the equation of the perpendicular bisector of the segment joining the points A (6, -3) and B (-2, 5)? How do you find the equation that is the perpendicular bisector of the line segment with endpoints (-2, 4) and (6, 8)? How do you construct perpendicular bisectors of a triangle? How do you find the perpendicular bisector of a line segment? How many perpendicular bisectors can be constructed for a line? A triangle has corners at (4 , 1 ), ( 2, 4 ), and ( 0, 2 )#. What are the endpoints of the triangle's perpendicular bisectors? A triangle has corners at (6 , 1 ), ( 4, 2 ), and ( 2, 8 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors? A triangle has corners at (5 , 4 ), ( 7, 1 ), and ( 1, 3 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors? A triangle has corners at (2 , 4 ), ( 3, 1 ), and ( 8, 3 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors? A triangle has corners at (2 , 2 ), ( 5, 6 ), and ( 1, 4 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors? A triangle has corners at (2 , 8 ), ( 2, 3 ), and ( 5, 4 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors? A triangle has corners at (2 , 5 ), ( 1, 3 ), and ( 8, 1 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors? A triangle has corners at (5 , 3 ), ( 7 ,8), and ( 2, 1 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors? A triangle has corners at (2 , 1 ), ( 5 , 6), and ( 8 , 5 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors? A triangle has vertices at A(a,b ), C(c,d), and O(0,0). What are the endpoints and length of the perpendicular bisector of AC ? A triangle has corners at (3,7), (4,1), and (8,2). What are the endpoints and lengths of the triangle's perpendicular bisectors? A triangle has corners at (8 , 4 ), ( 4 , 3), and ( 6 , 5 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors? A triangle has corners at (5 , 4 ), ( 7 , 9), and ( 5 , 8 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors? Question #0994c A line segment is bisected by line with the equation 6 y + 7 x = 4 . If one end of the line segment is at (2 ,4 ), where is the other end? A line segment is bisected by line with the equation 3 y - 3 x = 4 . If one end of the line segment is at (2 ,4 ), where is the other end? A line segment is bisected by line with the equation 3 y - 3 x = 1 . If one end of the line segment is at (2 ,5 ), where is the other end? A line segment is bisected by line with the equation 6 y - 2 x = 1 . If one end of the line segment is at (2 ,5 ), where is the other end? A line segment is bisected by line with the equation 6 y - 2 x = 1 . If one end of the line segment is at (4 ,1 ), where is the other end? A line segment is bisected by line with the equation 6 y - 7 x = 3 . If one end of the line segment is at (4 ,2 ), where is the other end? A line segment is bisected by line with the equation 6 y - 7 x = 3 . If one end of the line segment is at (7 ,2 ), where is the other end? A line segment is bisected by a line with the equation 3 y - 7 x = 3 . If one end of the line segment is at (7 ,8 ), where is the other end? A line segment is bisected by a line with the equation 3 y - 7 x = 2 . If one end of the line segment is at (7 ,8 ), where is the other end? A line segment is bisected by a line with the equation 3 y - 7 x = 2 . If one end of the line segment is at (7 ,3 ), where is the other end? A line segment is bisected by a line with the equation 3 y - 8 x = 2 . If one end of the line segment is at (1 ,3 ), where is the other end? A line segment is bisected by a line with the equation 7 y + x = 7 . If one end of the line segment is at (1 ,3 ), where is the other end? A line segment is bisected by a line with the equation 7 y + x = 1 . If one end of the line segment is at (1 ,6 ), where is the other end? A line segment is bisected by a line with the equation -3 y + x = 1 . If one end of the line segment is at (1 ,6 ), where is the other end? A line segment is bisected by a line with the equation -3 y + 7 x = 1 . If one end of the line segment is at (9 ,2 ), where is the other end? A line segment is bisected by a line with the equation - y + 7 x = 1 . If one end of the line segment is at (1 ,3 ), where is the other end? A line segment is bisected by a line with the equation - y + 3 x = 1 . If one end of the line segment is at (6 ,3 ), where is the other end? A line segment is bisected by a line with the equation - 2 y + 3 x = 1 . If one end of the line segment is at (6 ,3 ), where is the other end? A line segment is bisected by a line with the equation - 5 y + 3 x = 1 . If one end of the line segment is at (6 ,4 ), where is the other end? A line segment is bisected by a line with the equation - 5 y + 2 x = 1 . If one end of the line segment is at (6 ,4 ), where is the other end? A line segment is bisected by a line with the equation 5 y + 2 x = 1 . If one end of the line segment is at (6 ,4 ), where is the other end? A line segment is bisected by a line with the equation 5 y + 2 x = 1 . If one end of the line segment is at (3 ,4 ), where is the other end? A line segment is bisected by a line with the equation 5 y -4 x = 1 . If one end of the line segment is at (3 ,4 ), where is the other end? A line segment is bisected by a line with the equation 5 y -4 x = 1 . If one end of the line segment is at (3 ,8 ), where is the other end? A line segment is bisected by a line with the equation 2 y -4 x = 1 . If one end of the line segment is at (3 ,8 ), where is the other end? A line segment is bisected by a line with the equation 2 y + 9 x = 3 . If one end of the line segment is at (3 ,2 ), where is the other end? A line segment is bisected by a line with the equation 4 y + 9 x = 8 . If one end of the line segment is at (5 ,2 ), where is the other end? A line segment is bisected by a line with the equation 4 y + x = 8 . If one end of the line segment is at (5 ,2 ), where is the other end? A line segment is bisected by a line with the equation 4 y + x = 8 . If one end of the line segment is at (5 ,6 ), where is the other end? A line segment is bisected by a line with the equation 4 y + x = 3 . If one end of the line segment is at (5 ,6 ), where is the other end? A line segment is bisected by a line with the equation -7 y + x = 3 . If one end of the line segment is at (1 ,6 ), where is the other end? A line segment is bisected by a line with the equation -7 y + 5 x = 1 . If one end of the line segment is at (1 ,4 ), where is the other end? A line segment is bisected by a line with the equation -7 y + 3 x = 1 . If one end of the line segment is at ( 2 , 4 ), where is the other end? A line segment is bisected by a line with the equation -7 y + 3 x = 2 . If one end of the line segment is at ( 2 , 4 ), where is the other end? A line segment is bisected by a line with the equation -7 y + 3 x = 2 . If one end of the line segment is at ( 2 , 1 ), where is the other end? A line segment is bisected by a line with the equation -6 y + 3 x = 2 . If one end of the line segment is at ( 5 , 1 ), where is the other end? A line segment is bisected by a line with the equation -6 y + 9 x = 2 . If one end of the line segment is at ( 5 , 1 ), where is the other end? A line segment is bisected by a line with the equation -6 y - x = 3 . If one end of the line segment is at ( 5 , 1 ), where is the other end? A line segment is bisected by a line with the equation -6 y - x = 3 . If one end of the line segment is at ( 8 , 3 ), where is the other end? A line segment is bisected by a line with the equation - 2 y - x = 1 . If one end of the line segment is at ( 8 , 3 ), where is the other end? A line segment is bisected by a line with the equation - 2 y - x = 2 . If one end of the line segment is at ( 8 , 7 ), where is the other end? A line segment is bisected by a line with the equation - 2 y - 5 x = 2 . If one end of the line segment is at ( 8 , 7 ), where is the other end? A line segment is bisected by a line with the equation 2 y - 5 x = 2 . If one end of the line segment is at ( 4 , 8 ), where is the other end? A line segment is bisected by a line with the equation 2 y - 2 x = 2 . If one end of the line segment is at ( 3 , 8 ), where is the other end? A line segment is bisected by a line with the equation 4 y - 2 x = 3 . If one end of the line segment is at ( 5 , 6 ), where is the other end? A line segment is bisected by a line with the equation 3 y - 7 x = 2 . If one end of the line segment is at ( 8 , 1 ), where is the other end? A line segment is bisected by a line with the equation 6 y + 5 x = 2 . If one end of the line segment is at ( 5 , 8 ), where is the other end? A line segment is bisected by a line with the equation 3 y + 5 x = 2 . If one end of the line segment is at ( 5 , 8 ), where is the other end? A line segment is bisected by a line with the equation 3 y + 5 x = 2 . If one end of the line segment is at ( 1 , 4 ), where is the other end? A line segment is bisected by a line with the equation - 4 y + x = 1 . If one end of the line segment is at ( 7 , 2 ), where is the other end? A line segment is bisected by a line with the equation - y + 7 x = 1 . If one end of the line segment is at ( 7 , 2 ), where is the other end? A line segment is bisected by a line with the equation - y + 4 x = 3 . If one end of the line segment is at ( 2 , 6 ), where is the other end? A line segment is bisected by a line with the equation - 9 y + 4 x = 6 . If one end of the line segment is at ( 7 , 1 ), where is the other end? A line segment is bisected by a line with the equation - 3 y + 4 x = 6 . If one end of the line segment is at ( 3 , 1 ), where is the other end? A line segment is bisected by a line with the equation - 3 y + 6 x = 6 . If one end of the line segment is at ( 3 , 3 ), where is the other end? A line segment is bisected by a line with the equation - 3 y + 6 x = 5 . If one end of the line segment is at ( 3 , 3 ), where is the other end? A line segment is bisected by a line with the equation - 3 y + 2 x = 5 . If one end of the line segment is at ( 7 , 9 ), where is the other end? A line segment is bisected by a line with the equation - 3 y + 2 x = 2 . If one end of the line segment is at ( 7 , 9 ), where is the other end? A line segment is bisected by a line with the equation - 3 y + 5 x = 2 . If one end of the line segment is at ( 7 , 9 ), where is the other end? A line segment is bisected by a line with the equation - 3 y + 5 x = 8 . If one end of the line segment is at ( 7 , 9 ), where is the other end? A line segment is bisected by a line with the equation - 6 y + 5 x = 4 . If one end of the line segment is at ( 2 , 5 ), where is the other end? A line segment is bisected by a line with the equation - 6 y + 2 x = 4 . If one end of the line segment is at ( 4 , 8 ), where is the other end? A line segment is bisected by a line with the equation - 6 y + 2 x = 3 . If one end of the line segment is at ( 4 , 8 ), where is the other end? A line segment is bisected by a line with the equation - 6 y + x = 3 . If one end of the line segment is at ( 4 , 5 ), where is the other end? A line segment is bisected by a line with the equation 2 y + x = 7 . If one end of the line segment is at ( 5 , 3 ), where is the other end? A line segment is bisected by a line with the equation 2 y + 3 x = 3 . If one end of the line segment is at ( 1 , 8 ), where is the other end? A line segment is bisected by a line with the equation 4 y + 3 x = 8 . If one end of the line segment is at ( 1 , 8 ), where is the other end? A line segment is bisected by a line with the equation 4 y - 6 x = 8 . If one end of the line segment is at ( 1 , 8 ), where is the other end? A line segment is bisected by a line with the equation 4 y - 6 x = 8 . If one end of the line segment is at ( 8 , 3 ), where is the other end? A line segment is bisected by a line with the equation 4 y - 6 x = 8 . If one end of the line segment is at ( 7 , 3 ), where is the other end? A line segment is bisected by a line with the equation 4 y - 2 x = 5 . If one end of the line segment is at ( 7 , 3 ), where is the other end? A line segment is bisected by a line with the equation 9 y - 2 x = 5 . If one end of the line segment is at ( 7 , 3 ), where is the other end? A line segment is bisected by a line with the equation 9 y + x = 5 . If one end of the line segment is at ( 7 , 4 ), where is the other end? A line segment is bisected by a line with the equation 8 y + 5 x = 4 . If one end of the line segment is at ( 1 , 3 ), where is the other end? A line segment is bisected by a line with the equation 8 y + 5 x = 4 . If one end of the line segment is at ( 2 , 7 ), where is the other end? A line segment is bisected by a line with the equation 4 y - 3 x = 2 . If one end of the line segment is at ( 7 , 5 ), where is the other end? A line segment is bisected by a line with the equation 4 y - 3 x = 2 . If one end of the line segment is at ( 2 , 5 ), where is the other end? A line segment is bisected by a line with the equation 4 y - 3 x = 2 . If one end of the line segment is at ( 2 , 1 ), where is the other end? A line segment is bisected by a line with the equation 4 y + 3 x = 2 . If one end of the line segment is at ( 2 , 1 ), where is the other end? A line segment is bisected by a line with the equation 4 y + 3 x = 4 . If one end of the line segment is at ( 8 , 1 ), where is the other end? A line segment is bisected by a line with the equation 4 y + 3 x = 4 . If one end of the line segment is at ( 8 , 9 ), where is the other end? Describe and write an equation for the locus of points equidistant form A(a_x, a_y) and B(b_x,b_y)? Test what you derived for P_A(-2,5) and P_B(6,1)? Let A(x_a,y_a) and B(x_b,y_b) be two points in the plane and let P(x,y) be the point that divides bar(AB) in the ratio k :1, where k>0. Show that x= (x_a+kx_b)/ (1+k) and y= (y_a+ky_b)/( 1+k)? Let A be (−3,5) and B be (5,−10)). Find: (1) the length of segment bar(AB) (2) the midpoint P of bar(AB) (3) the point Q which splits bar(AB) in the ratio 2:5? Let l be a line described by equation ax+by+c=0 and let P(x,y) be a point not on l. Express the distance, d between l and P in terms of the coefficients a, b and c of the equation of line? In a triangle ABC (figure) the points P and Q are selected in the sides AC and BC respectively in a way that PC is half of BC and QC is half of AC:bar(PC)/bar(BC) = 1/2; bar(QC)/bar(AC)= 1/2. Find bar(PQ) if the side bar(Ab) is 20? In a triangle ABC, AB=AC and D is a point on side AC such that BCxBC=ACxCD. How to prove that BD=BC? This question combines geometry and algebra. Refer to the geometrical construction, find the unknown values? Maya drives from New York City to Boston at a rate of 40 MPH and drives at a rate of 60 MPH on the return trip. What was his average speed for the entire trip? Use the Harmonic mean to compute? Construct the HM geometrically? Using a compass and straight edge only mark two points A and B. Draw the line l through them and find another point C on l such that AB = BC? Draw a line l and a point A not lying on l. Draw the line m that is passing through A and parallel to l? Draw a line l and two points A and B not lying on l. Make sure that the line bar(AB) is not perpendicular to l. Find the point C on l such that AC = BC? Construct a regular pentagon using a compass and straight edge? Explain each step Given 2 numbers (a,b) it is possible to perform geometrically the following algebraic operations: a+b, a−b, a*b, a/b. Use only a straight edge and compass to show each operation? Constructing the angle 75°? Let P(x_1, y_1) be a point and let l be the line with equation ax+ by +c =0. Show the distance d from P->l is given by: d =(ax_1+ by_1 + c)/sqrt( a^2 +b^2)? Find the distance d of the point P(6,7) from the line l with equation 3x +4y =11? Let P(a,b) and Q(c,d) be two points in the plane. Find the equation of the line l that is the perpendicular bisector of the line segment bar(PQ)? Q is the midpoint of GH¯¯¯¯¯¯ , GQ=2x+3, and GH=5x−5 . What is the length of GQ¯¯¯¯¯ ? Given x^2 + 4x - 32 = 0 use geometric construction to determine roots? Generalize to ax^2+bx+c=0 finding a geometric interpretation of a quadratic formula (-b+- sqrt(b^2-4ac))/(2a)? Prove the diagonals of a parallelogram bisect each other, i.e. bar(AE) = bar(EC) and bar(BE) = bar(ED) ? On the figure given show that bar(OC) is sqrt(2)? Question #a55ba In a DeltaABC, right angled at A, a point D is on side AB. Prove that CD^2=BC^2+BD^2? Question #2b5bb Question #f11e4 Adina is constructing a line perpendicular to YJ←→. She has already constructed two arcs as shown. She moves her compass point to Y to construct an arc above the line. What must be true about the width of Adina’s compass opening before she draws the arc? Mayumi is constructing a line through point P that is perpendicular to RS←→. She places her compass on point P to construct an arc. What must be true about the width of the compass opening when Mayumi draws the arc? Natasha is constructing the bisector of PQ¯¯¯¯¯PQ¯. She has already constructed an arc as shown. What should Natasha do for her next step? ABC is a triangle whose sides AB = 6 cm, BC = 8 cm and AC = 12 cms. D is such a point situated on AC that angle ADB = angle ABC. Find the length of BD ? How to do this perpendicular bisector of a chord question? In triangle ABC, AB=AC.The circle through B touches the side AC at the mid-point D of AC, passes through a point P on AB. Prove that 4 ×AP = AB ? Question #43bfc Question #0583a Question #ad0e0 In a DeltaXYZ having X(-3,2), Y(-5,-6) and Z(-5,0), is perpendicular bisector of YZ same as median from X? Perpendicular bisectors of sides of a triangle are y=-x+4, y=-3x+6 and y=-1/2x+7/2. What is its centroid? Special Properties and Parts of Triangles View all chapters Perpendicular Bisectors Angle Bisectors Altitudes Medians and Centroids Next