Line ℓ has equation y= – x+4. Find the distance between ℓ and the point B( – 5,0).

Answer 1

Distance between (-5,0) and y = -x + 4 is a perpendicular line.

The slope of the line y = -x + 4 is -1, so the slope of the perpendicular line is 1.

equation of perpendicular line is y = mx + b, where m = 1.

to find b, substitute (-5,0) for (x,y) and solve for b - b = 5, so equation of perpendicular line is y = x + 5

to find point where perpendicular line and y = -x + 4 intersect, equate the equations of the two lines:

-x + 4 = x + 5

2x = -1

x = -1/2

since y = x + 5

y = 4 1/2

so point of intersection is (-1/2,4 1/2)

use distance formula to find distance between (-5,0) and (-1/2, 4 1/2)

Answer 2

Deteremine the equation of the line perpendicular to y = -x + 4 that passes through (-5, 0).

Determine the point of intersection of the two equations.

Determine the distance from point of intersection to (-5, 0)