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Without using Pythagora’s theorem, show that the points A(1, 2), B(4, 5) and C(6, 3) are the vertices of a right-angled triangle.

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The ΔABC is made up of three lines, AB,BC and CA

For a right angle triangle, two lines must be at 90° so they are perpendicular to each other.

Checking for lines AB and BC

For two lines to be perpendicular, their product of slope must be equal to -1.

Given points A(1, 2), B(4, 5) and C(6, 3)

Checking slopes of line AB and BC

1×-1 = -1

So AB is Perpendicular to BC.

So it is a right angle triangle.

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