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?

Question

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?

Sadie Allen · Accepted Answer

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