# The vertices of ΔABC are (—2, 1), (5, 4) and (2, —3) respectively. Find the area of the triangle and the length of the altitude through A.

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The vertices of ΔABC are (-2, 1), (5, 4) and (2, -3) respectively. Find the area of the triangle and the length of the altitude through A.

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Let A(-2, 1), B(5, 4) and C(2, -3) be the vertices of ΔABC.

Let AD be the altitude through A.

Area of ΔABC

But area cannot be negative

Therefore, Area of ΔABC = 20square units

We know that area of Δ

Therefore, Length of the altitude AD=40/√58