**Finding Missing Coordinate When the Given Points are Collinear :**

Here we are going to see, how to find the missing coordinate when the given points are collinear.

If three points A (x_{1}, y_{1}) B(x_{2}, y_{2}) and C(x_{3}, y_{3}) will be collinear if the area of triangle ABC = 0 .

**Question 1 :**

In each of the following, find the value of ‘a’ for which the given points are collinear.

(i) (2, 3), (4, a) and (6, –3)

**Solution :**

Since the given points are collinear, then area of triangle formed by these points = 0

(2a - 12 + 18) - (12 + 6a - 6) = 0

(2a + 6) - (6 + 6a) = 0

2a + 6 - 6 - 6a = 0

-4a = 0

a = 0

(ii) (a, 2 – 2a), (–a + 1, 2a) and (–4–a, 6–2a)

[2a^{2} + (-a + 1)(6 - 2a)+(-4 - a)(2 - 2a)] - [(-a + 1)(2 - 2a)+2a(-4 - a)+a(6 - 2a)] = 0

[2a^{2 }- 6a + 2a^{2 }+ 6 - 2a - 8 + 8a - 2a + 2a^{2}] - [-2a + 2a^{2 }+ 2 - 2a - 8a - 2a^{2} + 6a - 2a^{2}] = 0

(6a^{2} - 2a - 2) - (-2a^{2} - 6a + 2) = 0

6a^{2} + 2a^{2} - 2a + 6a -2 - 2 = 0

8a^{2} + 4a - 4 = 0

Dividing the entire equation by 4, we get

2a^{2} + a - 1 = 0

(2a - 1) (a + 1) = 0

a = 1/2 and a = -1

After having gone through the stuff given above, we hope that the students would have understood, "Finding Missing Coordinate When the Given Points are Collinear".

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