In the triangle ABC with vertices A(2, 3), B(4, -1) and C(1, 2) find the equation and the length of the altitude from the vertex A.

Given:

A(2, 3), B(4, -1) and C(1, 2).

To find:

The equation and the length of the altitude from the vertex A.

Concept Used:

Distance of a point from a line.

Explanation:

Equation of side BC:

x + y – 3 = 0

The equation of the altitude that is perpendicular to x + y – 3 = 0 is x – y + λ = 0.

Line x – y + λ = 0 passes through (2, 3).

2 – 3 + λ = 0

λ = 1

Thus, the equation of the altitude from the vertex A (2, 3) is x – y + 1 = 0.

Let d be the length of the altitude from A (2, 3).

d

d

Hence, the required distance is.

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