Find the distance between each given line and a point not on the line. Write your answers in exact form and as a decimal number rounded to the nearest hundredth.

Question

1. 2x – 5y = 10, (0, –6)

2. 8x – 4y = 12, (–5, 8)

Answer 1

Use the fact that the shortest distance between a point and a line is a line drawn from that point that is perpendicular to that line.

Find equation of line perpendicular to given line using negative reciprocal of slope of given line and given x,y point coordinates.

Equate two equations of lines to find intersecting x point coordinate and then substitute x value in either equation to find intersecting y point coordinate.

Use that intersecting x,y point coordinates and given x,y point coordinates to find distance between those two lines.