Q56 of 59 Page 178

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).

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. m1m2 = -1


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



Here, x1 = 3, x2 = -2, y1 = -4 and y2 = 6




⇒ m1 = -2


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



Here, x1 = -3, x2 = 9, y1 = 6 and y2 = -18




⇒ m2 = -2


∵ m1 = m2 = -2


and m1m2 = -2 × (-2) = -4 ≠ -1


So, the lines are parallel and not perpendicular


Hence, the given statement is FALSE


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