Line L has an equation Y=-4/3x+8/3. Find the difference between L and the point V(6,3)

Question

Find the distance between the line and the point

Answer 1

the perpendicular line is y=3/4x + b

plug in (6,3) to calculate b,

3 = (3/4)(6) + b

b = 3-9/2 = -3/2

the perpendicular line is y=(3/4)x - 3/2

find where that line intersects y=-4/3x + 8/3

(-4/3)x + 8/3 = (3/4)x - 3/2

-16x + 32 = 9x -18

25x = 50

x =5

y=(3/4)5 - 3/2 = 15/4 -6/4 = 9/4

find the distance from (5,9/4) to (6,3)

d^2 = 1 + 9/16 = 25/16

d = 5/4 = distance of the point to the line