Question

The area of the triangle whose vertices are (2,-3) (3,2) and (-2,5) is​

Answer 1

Given:-

• Vertices of the triangles:-
• (2, -3), (3, 2) and (-2, 5)

To Find:-

• The area of the triangle.

Solution:-

Firstly we have the given points as:-

• (2, -3)
• (3, 2)
• (-2, 5)

From these points we get the following:-

• x₁ = 2
• x₂ = 3
• x₃ = -2
• y₁ = -3
• y₂ = 2
• y₃ = 5

We already know:-

• Area of triangle = 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

Putting all the values in the formula:-

Area = 1/2[2(2 - 5) + 3{5 - (-3)} + {-2(-3 - 2)}]

= Area = 1/2[2 × (-3) + 3(5 + 3) + {(-2) × (-5)}]

= Area = 1/2[-6 + 3 × 8 + 10]

= Area = 1/2[-6 + 24 + 10]

= Area = 1/2[-6 + 34]

= Area = 1/2[28]

= Area = 14 sq.units

∴ Area of the triangle is 14 sq.units

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Important Points:-

We need to remember the meaning of x₁, x₂ .... y₁, y₂.

So:-

• x₁ = abscissa of the 1st point
• x₂ = abscissa of the 2nd point
• x₃ = abscissa of the 3rd point
• y₁ = ordinate of the 1st point
• y₂ = ordinate of the 2nd point
• y₃ = ordinate of the 3rd point

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