Worksheet on Co-ordinate Triangle

In the worksheet on co-ordinate triangle we need to find the area of a triangle where the three co-ordinates of the vertices are given.


Let us recall the formula for finding the area of a triangle formed by joining the three given points as follows; 

In terms of Cartesian co-ordinates the area of a triangle formed by joining the points (x₁, y₁), (x₂, y₂) and (x₃, y₃) is

½ | y₁ (x₂ - x₃) + y₂ (x₃ - x₁) + y₃ (x₁ - x₂) | sq. units 

or, ½ | x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂) | sq. units. 

In terms of polar co-ordinates (x₁, y₁), (x₂, y₂) and (x₃, y₃) of the vertices A, B, C respectively. 


∆ ABC = 1/2 | (x₁ y₂ + x₂ y₃ + x₃ y₁) - (x₂ y₁ + x₃ y₂ + x₁ y₃) | sq. units.

To learn more Click Here.

1. Find the area of the triangle whose vertices have co-ordinates:

(i) (3, 2), (5, 4), (2, 2)

(ii) (6, 2), (- 3, 4), (4, - 3)

(iii) (0, 0), (a cos α, a sin α), (a cos β, a sin β)

(iv) (a cos α, b sin α), (a cos β, a sin β) , (a cos γ, b sin γ)

(v) (at₁², 2at₁), (at₂², 2at₂), (at₃², 2at₃)

(vi) (ct₁, c/t₁), (ct₂, c/t₂), (ct₃, c/t₃).


2. The area of the triangle formed by joining the points (2, 7), (5, 1) and (x, 3) is 18 sq. units. Find x.


3. The polar co-ordinates of the vertices of a triangle are (1, 5π/6), (2, π/2) and (3, π/6); find the area of the triangle.


4. If the polar co-ordinates of the points A, B ,C, D be (2√2, π/4), (4/√3, 2π/3) and (2√2, -5π/4) respectively, then show that the points A, B, C are collinear.


Answers for the worksheet on co-ordinate triangle are given below to check the exact answers of the above questions for finding the area of a triangle.


Answers:

(i) 1 sq. units

(ii) 24.5 sq. units

(iii) a²/2 |sin⁡(α - β)| sq units

(iv) 2 ab |sin⁡ (α - β)/2 sin⁡ (β - γ)/2 sin (γ - α)/2| sq units

(v) a² |(t₁ - t₂)(t₂ - t₃)(t₃ - t₁)| sq units


2. 10 or (- 2)


3. 5√3/4 sq. units.


 Co-ordinate Geometry 






11 and 12 Grade Math 

From Worksheet on Co-ordinate Triangle to HOME PAGE




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.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Area of a Square and Rectangle | Area of Squares & Rectan

    Jul 19, 25 05:00 AM

    Area and Perimeter of Square and Rectangle
    We will practice the questions given in the worksheet on area of a square and rectangle. We know the amount of surface that a plane figure covers is called its area. 1. Find the area of the square len…

    Read More

  2. Area of Rectangle Square and Triangle | Formulas| Area of Plane Shapes

    Jul 18, 25 10:38 AM

    Area of a Square of Side 1 cm
    Area of a closed plane figure is the amount of surface enclosed within its boundary. Look at the given figures. The shaded region of each figure denotes its area. The standard unit, generally used for…

    Read More

  3. What is Area in Maths? | Units to find Area | Conversion Table of Area

    Jul 17, 25 01:06 AM

    Concept of Area
    The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc. A rectangle, a square, a triangle and a circle are all examples of closed pla…

    Read More

  4. Worksheet on Perimeter | Perimeter of Squares and Rectangle | Answers

    Jul 17, 25 12:40 AM

    Most and Least Perimeter
    Practice the questions given in the worksheet on perimeter. The questions are based on finding the perimeter of the triangle, perimeter of the square, perimeter of rectangle and word problems. I. Find…

    Read More

  5. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 16, 25 11:46 PM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More