What point is on the line that passes through point z and is perpendicular to line ab?

LIne AB ((-2 , 4) and (0, -4)

Slope = (4 + 4) / (-2 - 0) = 8 / -2 = -4

Equation of line A: y = -4x - 4

Perpendicular lines, slope is opposite and reciprocal so slope = 1/4

Passes through point Z(0, 2)

Equation y = 1/4 x + 2

when y = 0 , 1/4 x+ 2 = 0

1/4 x = - 2

x = -2 * 4

x = - 8

(-8 , 0)

Answer

(-8 , 0) is on the line that passes through point Z and is perpendicular to line AB