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Home  >>  CBSE XI  >>  Math  >>  Straight Lines
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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).

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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.
answered Jul 9, 2014 by thanvigandhi_1
 

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