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In the Triangle Abc with Vertices a (2, 3), B (4, –1) and C (1, 2), Find the Equation and Length of Altitude from the Vertex A. - Mathematics

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

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Solution

Let AD be the altitude of triangle ABC from vertex A.

Accordingly, AD⊥BC

The equation of the line passing through point (2, 3) and having a slope of 1 is

(y – 3) = 1(x – 2)

⇒ x – y + 1 = 0

⇒ – x = 1

Therefore, equation of the altitude from vertex A = – x = 1.

Length of AD = Length of the perpendicular from A (2, 3) to BC

The equation of BC is

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APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 10 Straight Lines
Q 17 | Page 228
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