Q16 of 66 Page 7

For what value of y are the points P(1, 4), Q(3, y) and R(–3, 16) are collinear?(CBSE 2014)

To show that the points are collinear, we show that the area of triangle is equilateral = 0


Δ = 0


Δ = 1/2{x1(y2−y3) + x2(y3−y1) + x3(y1−y2)}


⇒ Δ = 1/2{1(y–16) + 3 (16–4)–3 (4–y)} = 0


⇒ y–16 + 36–12 + 3y = 0


⇒ 8 + 4y = 0


⇒ 4y = –8


y = –2

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