Question 33

The points (2,2), (6,3) and (4,11) are vertices of :

Distance between (2,2) and (6,3) $$=\sqrt{\left(6-2\right)^2+\left(3-2\right)^2}=\sqrt{16+1}=\sqrt{17}$$

Distance between (4,11) and (6,3) $$=\sqrt{\left(6-4\right)^2+\left(3-11\right)^2}=\sqrt{16+1}=2\sqrt{17}$$

Distance between (2,2) and (4,11) $$=\sqrt{\left(4-2\right)^2+\left(11-2\right)^2}=\sqrt{16+1}=\sqrt{85}$$

Thus, the three sides of the triangle are $$\sqrt{17}$$, $$2\sqrt{17}$$, and $$\sqrt{85}$$. This is a right angled triangle as -

$$\left(\sqrt{17}\right)^2+\left(2\sqrt{17}\right)^2=\left(\sqrt{85}\right)^2$$

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