Question

A is (-2,1)
B is (6,5)
C is (4,k) are all vertices of a right angled triangle ABC. Angle ABC is the right angle.

Find an equation of a line that passes through A and C. Give your answer in the form ay+bx=c where a, b and c are integers

plz help

Answer 1

1) in order to solve this problem you must to obtain The value of K,  for it you know by definition  that the  horizontal slope  of the side BC  is zero ,

then m = Y2-Y/X2-X1,   0 = 5-K/4-6⇒0 = 5-K⇒K = 5

known this value for K   you ca find the equation of thE line that pass through  A and C

2) Following the same procedure in first place you calculate the slope with the points A(-2,1) Y C ( 4,5)

m= 5-1/4-(-2) = 2

now with any point  A  or C and the slope you obtain the line

A(-2,1)

y-y1 = m (x-x1) ,   Y-1= 2(X-(-2)⇒Y-1= 2X+4⇒Y=2X+4-1⇒Y =2X+3