Question
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.
✓
Answer
The equation of BC is $\text{y}+1=\frac{2+1}{1-4}(\text{x}-4)$ $\text{y}+1=-\text{x}+4$ $\text{x}+\text{y}-3=0$ $\text{AL}=\big|\frac{2+3-3}{\sqrt{1+1}}\big|$ $=\sqrt{2}$
Clearly, slope of BC having equation x + y - 3 = 0 is -1. So, slope of AL is 1. As it passes through A(2, 3) so, its equation is y - 3 = 1(x - 2) or x - y + 1 = 0
Clearly, slope of BC having equation x + y - 3 = 0 is -1. So, slope of AL is 1. As it passes through A(2, 3) so, its equation is y - 3 = 1(x - 2) or x - y + 1 = 0
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