# Question #040c8

##### 2 Answers

See the Explanation.

#### Explanation:

Use the **Slope-Point Form** to find the eqn. of reqd. line (which is,

the **Perpendicular Bisector of the Line Segment AB** ), to get,

Now, try to find out where you have committed mistake.

#### Explanation:

The coordinates of the midpoint are the

#color(blue)"average"# of the x and y coordinates of A and B.

#rArrM=[1/2(1-3),1/2(5+7)]=(-1,6)# We require to calculate the slope( m ) of AB using the

#color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#

where# (x_1,y_1),(x_2,y_2)" are 2 coordinate points"# The 2 points here are A(1 ,5) and B(-3 ,7)

let

# (x_1,y_1)=(1,5)" and " (x_2,y_2)=(-3,7)#

#rArrm_(AB)=(7-5)/(-3-1)=2/(-4)=-1/2# The slope of a line perpendicular to AB is

#color(blue)"the negative inverse"# of the slope of AB.

#rArrm_("perp")=-1/(m_(AB)#

#rArrm_("perp")=-1/(-1/2)=2# The equation of a line in

#color(blue)"point-slope form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#

where# (x_1,y_1)" are the coordinates of a point on the line"#

#"here "m_("perp")=2" and " (x_1,y_1)=M(-1,6)#

#rArry-6=2(x+1)# distributing and simplifying.

#y=2x+2+6#

#rArry=2x+8" is equation of perpendicular line"#