Question

Show that the points (2, 4), (0, 1) and (4,7) are collinear.
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Answer 1

The three points (2, 4), (0, 1) and (4, 7) are collinear, it is proved.

Step-by-step explanation:

We have,

The three points are (2, 4), (0, 1) and (4,7).

If the three points are colliner, then the area of traingle is zero(0).

Here, (x_1 = 2, y_1 = 4), (x_2 = 0, y_2 = 1) and (x_3 = 4, y_3 = 7).

∴ x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) =0

⇒ 2(1 - 7) + 0 (7 - 4) + 4 (4 - 1) = - 12 + 0 + 12

= - 12 + 12 = 0, it is proved.

Answer 2

Answer:

Step-by-step explanation

When the points A, B, and C are collinear, the area of the triangle is zero.

If the points A, B and C are collinear.  

The condition for points to be collinear is

 $1/2 \ [ x_1(y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2)] = 0$

The area of the triangle formed by joining the given points

= 1/2 [(2 (1-7) +0 (7 -4) + 4(4-1)]

= 1/2 (-12 + 12) = 0.

Since the area of the triangle formed by joining the given points is zero, hence the given points are collinear.

Hence Proved