To orrow exam and i dont know how to solve them? Pls heeeellllppp

17.       In a triangle ABC has vertices A( 3 , 5 ) , B( 2 , 3 ) , and C( 5 , 2 ).  Find the equation of the altitude from A to BC.
 
 
18.       Find the equation of the median from vertex A in a triangle ABC, if the coordinates of the vertices are
A( -3 , -1 ) , B( 3 , 5 ) , and C( 7 , -3 ).
 
19.       Find the equation of the perpendicular bisector of the line segment joining P( -1 , 4 ) to Q( 3 , -2 ).

a)

Altitude is perpendicular drawn from a vertex to opposite side.

let the altitude = AB from A to BC

AD and BC are perpendicular

B = (2, 3) and C = (5, 2)

Slope of BC = (2 - 3) /(5 - 2) = -1/3

slope of AD = -1 /(-1/3) = 3

AD passes through A(3, 5)

Equation of AD with slope 3 and passing through (3, 5) is

y - 5 = 3 (x - 3)

y = 3x - 4

You can solve the remaining two on your own

Median is line drawn from vertex to mid point of opposite side.
Mid point of (x1, y1) and (x2, y2) is (x1 + x2)/2 and (y1 + y2)/2
If AD is median, you know coordinates of A and mid point of BC. You can find out slope and equation of AD

Perpendicular bisector is perpendicular drawn from mid point of side.
Find out slope of PQ
find out slope of perpendicular bisector ( negative reciprocal of PQ)
find out mid point of PQ
Find out equation required line.