# Worksheet on Collinear Triangle

The questions given in the worksheet on collinear triangle, the area of a triangle is always 0. We know, when area of a triangle is 0 then the three vertices of the triangle is in the same line and these triangles are known as collinear.

Let us recall the condition of collinear triangle as follows;

The area of a collinear triangle formed by joining the points (x₁, y₁), (x₂, y₂) and (x₃, y₃) is y₁ (x₂ - x₃) + y₂ (x₃ – x₁) + y₃ (x₁ – x₂)= 0, which is the required condition of collinearity of-the three given points.

1. Show that the following sets of points are collinear :

(i) (0, - 2), (2, 4) and (- 1, - 5)

(ii) (3, - 2), (- 5, 4) and (- 1, 1)

(iii) (3a, 0), (0, 3b) and (a, 2b).

2. If the points (1, 2), (2, 4) and (t, 6) be collinear, find the value of t.

3. If the points (a, 0), (0, b) and (1, 1) are collinear, then show that 1/a + 1/b = 1

4. For what value of k the points (1, - 1), (2, 1) and (k, 5) shall be on the same straight line ?

5. (i) Find the area of the triangle having vertices (1, 4), (- 1, 2) and (- 4, - 1). Interpret the result.

(ii) Find the area of the triangle having vertices (a, b + c), (b, c + a) and (c, a + b) and interpret the result geometrically.

6. (i) Show that the straight line joining the points (- 3, 2) and (6, - 4) passes through the origin.

(ii) Prove that the points (-4, - 5), (9, 8) and the mid-point of the line-segment joining the points (2, 1) and (6, 5) are on the same straight line.

7. Examine the collinearity of the points (2, 3), (4, 5) and (6, 5).

8. Find the value of m for which the area of the triangle having vertices at (-1, m), ( m - 2, 1) and (m - 2, m) is 12¹/₂ sq, units.

9. Show that the three distinct points(p, p²) ,(q, q²) and (r, r²) can never be collinear.

Answers for the worksheet on collinear triangle are given below to check the exact answers of the above questions.

2. 3

4. 4

5. (i) 0; the given points are collinear

(ii) 0; the given points are collinear

7. No

8. 6 or, (- 4)

Co-ordinate Geometry

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