A triangle has corners A, B, and C located at #(2 ,7 )#, #(3 ,5 )#, and #(9 , 4 )#, respectively. What are the endpoints and length of the altitude going through corner C?

1 Answer
Chirag Mehta
Dec 25, 2017

#(23/5,9/5),(9,4)#

Explanation:

#A (2,7) B (3,5)#.
Find the equation of line AB
We know that
#y-y_1=m (x-x_1)##{where ( m=(y_2 - y_1)/(x_2 - x_1))}#
plugging in values we get
#color (green)(y+2x=11)#
perpemdicular from C would either be on AB or AB extended.
equation of line perpendicular to this can be found using
#y=(m')x+b# #m'=-1/m#(m is what we used to find equation of AB.
SO, #y=(1/2)x+b#
#b# can be found by using co-ordinates of C
#4=9/2 +b#
#b=-1/2#
now equation looks like
#y=x/2-1/2#
#2y=x-1#
#2y-x=-1#
#color(green) (x-2y=1)#

we need to find end points of altitude from C, one can be easily found or say it is known , it is co-ordinates of C itself that is #(9,4)#

to find other end co-ordimates , solve the to 2 equations that we got represented in green color , i am leaving that part to be solved by you . however i would give answer that is #(23/5,9/5)#

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