Question

Line v passes through points (1, 12) and (10, 7). Line w is perpendicular to v. What is the slope of line w?

Answer 1

Line v passes through points (1, 12) and (10, 7). The slope of line w as improper fraction is $\frac{9}{5}$

Solution:

Given, two points are (1, 12) and (10, 7)  

We have to find the slope of a line that is perpendicular to line passing through the above given two points.

Slope of a line that pass through $\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)$ is given as:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text { Here, in our problem, } x_{1}=1, y_{1}=12 \text { and } x_{2}=10, y_{2}=7$

$\text { slope } m=\frac{7-12}{10-1}=\frac{-5}{9}$

So, slope of line v is $\frac{-5}{9}$

Since line w is perpendicular to v, the product of their slopes equals -1

$\text { slope line } v \times \text { slope of line } w=-1$

$\frac{-5}{9} \times \text { slope of line } w=-1$

$\text { Slope of line } w=\frac{9}{-5} \times(-1)=\frac{9}{5}$

Hence, the slope of line w as improper fraction is $\frac{9}{5}$