What is the area of a triangle whose vertices are R(-4, 2),S(1, 2), and T(-5, -4)?

Solution:

Consider R(−4, 2),S(1, 2), and T(−5, −4) as the vertices of △ RST

x₁ = - 4, y₁ = 2

x₂ = 1, y₂ = 2

x₃ = - 5, y₃ = - 4

We know the formula for the area of the triangle in coordinate geometry as:

Area of △ RST = 1/2 |(x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃(y₁ - y₂)|

Substituting the values

= 1/2 |-4 (2 - (-4)) + 1 (- 4 - 2) + (-5) (2 - 2)|

By further calculation

= 1/2 |-24 - 6 - 0|

= 1/2 |-30|

So we get

= 30/2

= 15 sq.units

Therefore, the area of the triangle is 15 sq. units.

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What is the area of a triangle whose vertices are R(-4, 2),S(1, 2), and T(-5, -4)?

Summary:

The area of a triangle whose vertices are R(-4, 2),S(1, 2), and T(-5, -4) is 37.5 sq. units.