Geometry IXL find the distance

Question

Line L has equation y=x-4. Find the distance between L and the point (-7,0)

Answer 1

y = x - 4 is how far from (-7,0)

the perpendicular line through the same point is: y=-x + b Plug in the point to find b

0 =7 +b

b =-7

the perpendicular line is y=-x -7

set them equal

-x-7 = x -4

2x = -3

x = -3/2

y = 3/2-7 = -11/2

the intersection point is (-3/2,-11/2

find the distance from (-7,0) to (-3/2, -11/2)

d^2 = (11/2)^2 + (11/2)^2 = 2(121/4) = 121/2 = 60.5

d = sqr60.5 = about 7.78 = distance between the line and the point

It may help to sketch the graph of the line and plot the point, and construct a right triangle with 2 sides each = 5.5, and solve for the hypotenuse = 5.5sqr2 = about 7.78