Browse Questions

State whether the following is true or false and justify : Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).

Toolbox:
• Slope of a line joining the points $(x_1, y_1)$ and $(x_2, y_2)$ is $\bigg( \large\frac{y_2-y_1}{x_2-x_1} \bigg)$
• If two lines are perpendicular then the product of their slopes $m_1m_2 = -1.$
Step 1 :
Slope of the line joining the points (3, -4) and (-2, 6) is
$m_1 = \large\frac{y_2-y_1}{x_2-x_1}$$= \large\frac{6-(-4)}{-2-3}$$ = \large\frac{10}{-5}$
$=-2$
Slope of the line joining (-3, 6) and (9, -18) is
$m_2 = \large\frac{-18-6}{9-(-3)}$$= \large\frac{-24}{12}$$=-2$
If two lines are perpendicular, then the product of their slopes is -1.
( i.e ) $m_1m_2=-1$
But let $m_1m_2 = 4$
Hence the statement is falser.