A, B and C have co-ordinates (0, 3), (4, 4) and (8, 0) respectively. Find the equation of the line through A and perpendicular to BC.

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Solution

Slope of BC = $fraction numerator 0 minus 4 over denominator 8 minus 4 end fraction equals negative 1$

Slope of line perpendicular to BC = $fraction numerator negative 1 over denominator s l o p e space o f space B C end fraction equals 1$

The equation of the line through A and perpendicular to BC is given by:

y - y₁ = m(x - x₁)

y - 3 = 1(x - 0)

y - 3 = x

y = x + 3

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