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Question
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.
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Solution
Let the given points be A(4, 4), B(3, 5) and C(–1, –1), then
slope of AB = `("y"_2 - "y"_1)/("x"_2 - "x"_1)`
= `(5 - 4)/(3 - 4)`
= `1/(-1)`
= −1 = m1
Slope of BC = `(-1 - 5)/(3 - 4)`
= `(-6)/(-4)`
= `3/2`
Slope of CA = `(4 + 1)/(4 + 1)`
= `5/5`
= 1 = m2
Slope of AB × Slope of CA = m1 × m2
= −1 × 1
= −1
Hence, AB ⊥ CA
= A, B, C are the vertices of a right triangle.
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