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Question
Without using Pythagoras theorem show that points A(4, 4), B(3, 5) and C(−1, −1) are the vertices of a right angled triangle.
Solution
Given, A(4, 4), B(3, 5), C(−1, −1).
Slope of AB = `(y_2 - y_1)/(x_2 - x_1) = (5 - 4)/(3 - 4)` = −1
Slope of BC = `(-1 - 5)/(-1 - 3) = (-6)/(-4) = 3/2`
Slope of AC = `(-1 - 4)/(-1 - 4)` = 1
Slope of AB x slope of AC = −1 × 1 = −1
∴ side AB ⊥ side AC
Thus ΔABC is a right angled triangle right angled at A.
∴ The given points are the vertices of a right angled triangle.
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