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. 

To learn more about collinear triangle, condition of collinearity and examples Click Here.

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.

Answers:

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 

• What is Co-ordinate Geometry?
  
• Rectangular Cartesian Co-ordinates
  
• Polar Co-ordinates
  
• Relation between Cartesian and Polar Co-Ordinates
  
• Distance between Two given Points
  
• Distance between Two Points in Polar Co-ordinates
  
• Division of Line Segment: Internal & External
  
• Area of the Triangle Formed by Three co-ordinate Points
  
• Condition of Collinearity of Three Points
  
• Medians of a Triangle are Concurrent
  
• Apollonius' Theorem
  
• Quadrilateral form a Parallelogram 
  
• Problems on Distance Between Two Points 
  
• Area of a Triangle Given 3 Points
  
• Worksheet on Quadrants
  
• Worksheet on Rectangular – Polar Conversion
  
• Worksheet on Line-Segment Joining the Points
  
• Worksheet on Distance Between Two Points
  
• Worksheet on Distance Between the Polar Co-ordinates
  
• Worksheet on Finding Mid-Point
  
• Worksheet on Division of Line-Segment
  
• Worksheet on Centroid of a Triangle
  
• Worksheet on Area of Co-ordinate Triangle
  
• Worksheet on Collinear Triangle
  
• Worksheet on Area of Polygon
  
• Worksheet on Cartesian Triangle

11 and 12 Grade Math 

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