Maths / Coordinate Geometry / Distance Formula

QUESTION
 

Prove that the points (4,4),(3,5) and (-1,-1) are the vertices of a right angled triangle.

EXPLANATION
Explain TypeExplanation Content
Text

Let the points (4,4) , (3,5) and (-1,-1) be denoted by P, A and R , respectively.

Now large PQ =sqrt{(3-4)^2+(5-4)^2}=sqrt{2}

        large QR =sqrt{(-1-3)^2+(-1-5)^2}=sqrt{52}

and large PR =sqrt{(-1-4)^2+(-1-4)^2}=sqrt{50}

We observe that the sum of square of two sides , PQ and PR ids equal to the square of the third side QR i.e.,

QR^2=PR^2+PQ^2

If follows from the converse of the Pythagoras theorem that the triangle PQR is a right triangle and the right angle is at P.

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