Question

How do you find the slope of a line perpendicular to V(3, 2), W(8, 5)?

Answer 1

See a solution process below:

Explanation:

First, find the slope of the line V-W. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(5) - color(blue)(2))/(color(red)(8) - color(blue)(3)) = 3/5`

Now, let's call the slope of the perpendicular line `m_p`

The slope of a perpendicular line is the negative inverse of the slope of the line it is perpendicular to, or:

`m_p = -1/m`

Substituting for `m` gives:

`m_p = -1/(3/5)`

`m_p = -5/3`

The slope of the line perpendicular to V-W is `-5/3`

Answer 2

`m=-5/3`

Explanation:

`"to calculate the slope of the line VW use the "color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1),(x_2,y_2)" are 2 coordinate points"`

`"the points are " (x_1,y_1)=(3,2),(x_2,y_2)=(8,5)`

`rArrm_(color(red)(VW))=(5-2)/(8-3)=3/5`

`" the slope of a line perpendicular to VW is"`

`m_(color(red)"perpendicular")=-1/m_(color(red)(VW))`

`rArrm_(color(red)"perpendicular")=-1/(3/5)=-5/3`