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?

Answer 1

`(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)`