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.
(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.
Sep 15, 24 04:57 PM
Sep 15, 24 04:08 PM
Sep 15, 24 03:16 PM
Sep 14, 24 04:31 PM
Sep 14, 24 03:39 PM
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.