line A passes through (2, -3) & (7, 2) & line B passes through (-3, 7) &(2, 2). Show A and B are perpendicular.

Question

Suppose line A passes through points (2, -3) and (7, 2) and line B passes through (-3, 7) and (2, 2). Show, algebraically, that lines A and B are perpendicular.

Answer 1

Find the slope of the A.

(2, -3) and (7, 2)

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m1 = (2-(-3))/(7-2)

      =5/5

       =1

Find the slope of the B.

(-3, 7) and (2, 2)

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m2 = (2-(-3))/(2-7)

      =5/-5

       =-1

m1*m2 = -1

So A and B are perpendicular.