What is the slope of any line perpendicular to the line passing through $(3, - 2)$ $(3,-2)$ and $(12, 19)$ $(12,19)$ ?

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What is the slope of any line perpendicular to the line passing through $(3, - 2)$ $(3,-2)$ and $(12, 19)$ $(12,19)$ ?

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Answer 1 · 2016-02-10T14:13:44

Slope of any line perpendicular to the line passing through $(3, - 2)$ $(3,−2)$ and $(12, 19)$ $(12,19)$ is $- \frac{3}{7}$ $-3/7$

Explanation:

If the two points are $(x_{1}, y_{1})$ $(x_1, y_1)$ and $(x_{2}, y_{2})$ $(x_2, y_2)$ , the slope of the line joining them is defined as

$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $(y_2-y_1)/(x_2-x_1)$ or $\frac{y_{1} - y_{2}}{x_{1} - x_{2}}$ $(y_1-y_2)/(x_1-x_2)$

As the points are $(3, - 2)$ $(3, -2)$ and $(12, 19)$ $(12, 19)$

the slope of line joining them is $\frac{19 - (- 2)}{12 - 3}$ $(19-(-2))/(12-3$ or $\frac{21}{9}$ $21/9$

i.e. $\frac{7}{3}$ $7/3$

Further product of slopes of two lines perpendicular to each other is $- 1$ $-1$ .

Hence slope of line perpendicular to the line passing through $(3, - 2)$ $(3,−2)$ and $(12, 19)$ $(12,19)$ will be $- \frac{1}{\frac{7}{3}}$ $-1/(7/3)$ or $- \frac{3}{7}$ $-3/7$ .

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What is the slope of any line perpendicular to the line passing through $(3, - 2)$ $(3,-2)$ and $(12, 19)$ $(12,19)$ ?

1 Answer

Explanation:

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What is the slope of any line perpendicular to the line passing through $(3, - 2)$ $(3,-2)$ and $(12, 19)$ $(12,19)$ ?