Q. 565.0( 1 Vote )

# State whether the statements are true or false.

Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).

Answer :

Given points are (3, -4), (-2, 6), (-3, 6) and (9, -18)

Now, we find the slope because if the lines are perpendicular then the product of the slopes is -1 i.e. m_{1}m_{2} = -1

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

Here, x_{1} = 3, x_{2} = -2, y_{1} = -4 and y_{2} = 6

⇒ m_{1} = -2

Now, slope of the line joining the points (-3, 6) and (9, -18)

Here, x_{1} = -3, x_{2} = 9, y_{1} = 6 and y_{2} = -18

⇒ m_{2} = -2

∵ m_{1} = m_{2} = -2

and m_{1}m_{2} = -2 × (-2) = -4 ≠ -1

So, the lines are parallel and not perpendicular

Hence, the given statement is **FALSE**

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