# 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

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Adding 1-Digit Number | Understand the Concept one Digit Number

Sep 17, 24 02:25 AM

Understand the concept of adding 1-digit number with the help of objects as well as numbers.

2. ### Counting Before, After and Between Numbers up to 10 | Number Counting

Sep 17, 24 01:47 AM

Counting before, after and between numbers up to 10 improves the child’s counting skills.

3. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 17, 24 12:10 AM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

4. ### Arranging Numbers | Ascending Order | Descending Order |Compare Digits

Sep 16, 24 11:24 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…