Question

If the points (1,1) (2,3) and (5,-1) form a right-angled triangle, then the hypotenuse is of length

• A. 3
• B. 6
• C. 4
• D. 5

Answer 1

Answer: (D)

We use the distance formula, i.e.

$Distancebetweentwopoints(x_1,y_1)\&(x_2,y_2)isd=\sqrt{{(x}_2-x_1{)}^2(-{y_2-y_1)}^2}$

Given points $A=(1,1),B=(2,3),C=(5,-1)$

Therefore,
$AB=\sqrt{{(1-2)}^2+{(1-3)}^2}=5$
$BC=\sqrt{{(2-5)}^2+{(3+1)}^2}=25$
$AC=\sqrt{{(1-5)}^2+{(1+1)}^2}=20$

$BC$ is larger side hence hypotenuse.

Hypotenuse is $BC=5$