Find the distance

Question

line l has equation y=x-4. find the distance between l and the point q (0,7)

Answer 1

y=x-4

distance between that line and point q(0,7) =

the perpendicular line through (0,7) is y=-x +7

the lines intersect when x-4 = -x+7

2x = 11

x =11/2 = 5.5

y = 1.5

intersection point is (5.5, 1.5)

find the distance between (5.5, 1.5) and (0,7)

d^2 = 5.5^2 +5.5^2 = 2(30.25) = 60.5

d = sqr60.5) = 7.778

d= about 7.8 = distance from the line to point q

it may help to graph the line and plot the point