Question

Line p passes through points (5,−3) and (−2, 5) . What is the slope of a line perpendicular to p ?

Answer 1

`\displaystyle (7)/(8)`

Explanation:

Hi there!

First, find the slope of Line p:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)` where two points that fall on the line are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (5,−3) and (−2, 5):

`\displaystyle m=(-3-5)/(5-(-2))\\\\\displaystyle m=(-3-5)/(5+2)\\\\\displaystyle m=(-8)/(7)`

Therefore, the slope of Line p is
`\displaystyle- (8)/(7)`.

Perpendicular lines always have slopes that are negative reciprocals, such as 1/2 and -1/2, and 3/4 and -4/3.

Knowing this, the slope of a line perpendicular to Line p would be the negative reciprocal of
`\displaystyle- (8)/(7)`, which is
`\displaystyle (7)/(8)`.

I hope this helps!