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 $\dpi{120} \large PR =\sqrt{(-1-4)^2+(-1-4)^2}=\sqrt{50}$

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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