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. Subtracting Integers | Subtraction of Integers |Fundamental Operations

    Jun 13, 24 02:51 AM

    Subtracting integers is the second operations on integers, among the four fundamental operations on integers. Change the sign of the integer to be subtracted and then add.

    Read More

  2. Properties of Subtracting Integers | Subtraction of Integers |Examples

    Jun 13, 24 02:28 AM

    The properties of subtracting integers are explained here along with the examples. 1. The difference (subtraction) of any two integers is always an integer. Examples: (a) (+7) – (+4) = 7 - 4 = 3

    Read More

  3. Math Only Math | Learn Math Step-by-Step | Worksheet | Videos | Games

    Jun 13, 24 12:11 AM

    Presenting math-only-math to kids, students and children. Mathematical ideas have been explained in the simplest possible way. Here you will have plenty of math help and lots of fun while learning.

    Read More

  4. Addition of Integers | Adding Integers on a Number Line | Examples

    Jun 12, 24 01:11 PM

    Addition of Integers
    We will learn addition of integers using number line. We know that counting forward means addition. When we add positive integers, we move to the right on the number line. For example to add +2 and +4…

    Read More

  5. Worksheet on Adding Integers | Integers Worksheets | Answers |Addition

    Jun 11, 24 07:15 PM

    Worksheet on Adding Integers
    Practice the questions given in the worksheet on adding integers. We know that the sum of any two integers is always an integer. I. Add the following integers:

    Read More