Q4 of 53 Page 107

Verify that points P(-2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle.

In a right angles triangle ABC, right angled at B, according to the pythagoras theorem

AB2 + BC2 = AC2


According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by
 .....(1)


For the given points Distance between P and Q is


PQ = =


QR = =


PR = = =


PQ2 = 16


QR2 = 25


PR2 = 41


As PQ2 + QR2 = PR2


Hence the given points form a right angled triangle.


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Determine whether the points are collinear.

(1) A(1, -3), B(2, -5), C(-4, 7)


(2) L(-2, 3), M(1, -3), N(5, 4)


(3) R(0, 3), D(2, 1), S(3, -1)


(4) P(-2, 3), Q(1, 2), R(4, 1)

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