What is the area of a triangle with vertices at (-2, 1), (2, 1), and (3, 4)? 

Solution:

We know that

Area of triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃)

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

(-2, 1), (2, 1), and (3, 4) are the given vertices

Substituting it in the formula we get

Area of triangle with vertices (-2, 1), (2, 1), and (3, 4)

= 1/2 [ -2 (1 - 4) + 2 (4 - 1) + 3 (1 - 1)]

By further calculation

= 1/2[-2(-3) + 2(3) + 3(0)]

= 1/2 [6 + 6]

= 1/2(12)

= 6 sq.units

Therefore, the area of the triangle is 6 sq.units.

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What is the area of a triangle with vertices at (-2, 1), (2, 1), and (3, 4)?

Summary:

The area of a triangle with vertices at (-2, 1), (2, 1), and (3, 4) is 6 sq. units.