Q13 of 157 Page 753

Show that the following points are collinear:

A(8, 1), B(3, –4) and C(2, –5)


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)}


⇒ 1/2{8(–4 + 5) + 3 (–5–1) + 2 (1 + 4)}


⇒ 1/2{8–18 + 10}


= 0


Hence collinear.


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13

Show that the following points are collinear:

A(–5, 1), B(5, 5) and C(10, 7)

 13

Show that the following points are collinear:

A(5, 1), B(1, –1) and C(11, 4)

 14

Find the value of x for which the points A(x, 2), B(–3, –4) and C(7, –5) are collinear.

 15

For what value of x are the points A(–3, 12), B(7, 6) and C(x, 9) collinear?