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KIM [24]
3 years ago
11

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

Mathematics
1 answer:
Firlakuza [10]3 years ago
8 0

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

<u>Solution:</u>

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<em> </em>line w is perpendicular to v,<em> the product of their slopes equals -1</em>

\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}

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