Question

Given two points M & N on the coordinate plane, find the slope of MN , and state the slope of the line perpendicular to MN . (there's two questions)

1) M(9,6), N(1,4)

2) M(-2,2), N(4,-4)

Answer 1

Problem 1)
`m = (1)/(4)`
`slope_(perpendicular) = -4`

Problem 2)
`m = (1)/(3)`
`slope_(perpendicular) = -3`

Explanation:

`slope = m = (y_2 - y_1)/(x_2 - x_1)`

`slope_(perpendicular) = (-1)/(m)`

Problem 1) M(9,6), N(1,4)

`slope = m = (6 - 4)/(9 - 1) = (2)/(8) = (1)/(4)`

`slope_(perpendicular) = (-1)/((1)/(4)) = -4`

Problem 2) M(-2,2), N(4,-4)

`slope = m = (4 - 2)/(4 - (-2)) = (2)/(6) = (1)/(3)`

`slope_(perpendicular) = (-1)/((1)/(3)) = -3`