Line ℓ has equation y= - 2/9 x– 2/3 . Find the distance between ℓ and the point E( - 4,4).

Answer 1

Perpendicular to l and eats (-4,4)

Slope of the perpendicular line is 9/2

B = 4 - (9/2)(-4) = 4 - (-18) = 22

y = (9/2)x + 22

They meet at (9/2)x + 22 = (-2/9)x - 2/3

81x + 396 = -4x - 12

85x = -408

x = -408/85 = -4.8

The intersection point is (-4.8, 0.4)

(-4,4)

sqrt [ (-0.8)^2 + (3.6)^2] = 3.687