Question

Which two pairs of points lie on perpendicular lines?

a. (-6,-8),(7,18)
b. (6,4),(4,12)
c. (-4,6),(2,3)

Answer 1

(-6,-8),(7,18) and (-4,6),(2,3) lie on perpendicular lines

Explanation:

we know that

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

step 1

Find the slope of the pair (-6,-8),(7,18)

substitute

`m=(18+8)/(7+6)`

`m=(26)/(13)`

`m=2`

step 2

Find the slope of the pair (6,4),(4,12)

substitute

`m=(12-4)/(4-6)`

`m=(8)/(-2)`

`m=-4`

step 3

Find the slope of the pair (-4,6),(2,3)

substitute

`m=(3-6)/(2+4)`

`m=(-3)/(6)`

`m=-(1)/(2)`

step 4

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

In this problem

`m=2` and
`m=-(1)/(2)` are opposite reciprocal

therefore

(-6,-8),(7,18) and (-4,6),(2,3) lie on perpendicular lines