Do the points represent the vertices of a right triangle (1,-4) (5,6) (-2,3)?

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Answer 1 · 2017-07-27T12:59:27

The $Delta$ is an isosceles right triangle, right-angled at the pt.

$(-2,3).$

Let us name the given Points (pts.) $A,B, and, C,$ resp.

We use the Notation $AB$ to denote the Distance between

the pts. $A and B.$

Using the Distance Formula, we find that,

$AB^2=(1-5)^2+(-4-6)^2=16+100=116;$

$BC^2=(5+2)^2+(6-3)^2=49+9=58;$ and,

$AC^2=(1+2)^2+(-4-3)^2=9+49=58.$

Clearly, $BC=AC, and, BC^2+AC^2=AB^2.$

Therefore, we conclude that, $DeltaABC$ is an isosceles right

triangle, right-angled at the pt. $C.$