Question

line P contains points A(-7,-9) and B(4,0). Line q is parallel to line p. Line r is perpendicular to line q. What is the slope of line r? Explain.

Answer 1

find slope of line p
y-y
x-x
then take opposite reciprocal

Answer 2

\[\frac{ y-y }{ x-x }\]

Answer 3

If two lines are parallel, it means they have the same slope. That being said, P and Q each have the same slope. This also means that if r is perpendicular to q, then it is also perpendicular to p. A line has a perpendicular slope if its slope is the negative reciprocal of the other line. Slope is (y2 - y1)/(x2-x1) So for the line you have, you have a slope of (0-9)/(4-(-7)) = -9/11. So if P has a slope of -9/11, then a perpendicular slope has to be the negative reciprocal, meaning that the slope of r is 11/9

Answer 4

Thank you so much! :)