Line joining the points $(3, - 4)$ and $(- 2, 6)$ is perpendicular to the line joining the points $(- 3, 6)$ and $(9, - 18)$ . State whether the statement is true or false. Justify.

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Solution

Slope of line joining the points $(3, - 4)$ and $(- 2, 6)$ is

$m_{1} = \frac{- 4 - 6}{3 + 2} = - 2$

Slope of line joining the points

$(- 3, 6)$ and $(9, - 18)$ is

$m_{1} = \frac{6 + 18}{- 3 - 9} = - 2$

Since, $m_{1} \times m_{2} = 4 \neq - 1$

Hence, the given lines are not perpendicular.

Hence, the given statement is false.

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