Question

. ABC is an equilateral triangle of side 3 units. The points P, Q lie on BC, CA respectively and are such that AQ = CP = 2units. If the point R lies on AB produced so that BR = 1unit, prove that P, Q, R are collinear

Answer 1

Points P, Q and R are collinear

Explanation:

To prove that two or three points are collinear the slope of any two pairs of point have to be the same

From the given question

AR = AQ = CP = 2 units

BR = BP = CQ = 1 unit

For line AB we have ; AR , BR . hence slope of line = BR / AR = 1/2

For line BC we have ; BP , CP . hence slope of line = CP / BP = 2/1

For Line AC we have ; AQ , CQ . hence slope of line = CQ / AQ = 1/2

slope of Line AB = slope of Line AC hence points P, Q and R are collinear