Question

4. Verify that points P(-2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle .​

Answer 1

Given ,

• The vertices of a triangle are P(-2, 2), Q(2, 2) and R(2, 7)

We know that , The distance between two points is given by

$\boxed{ \sf{D = \sqrt{ {(x_{2} - x_{1} )}^{2} +{(y_{2} - y_{1} )}^{2} } }}$

Thus ,

$\sf \mapsto PQ = \sqrt{ {(2 - ( - 2))}^{2} + {(2 - 2)}^{2} } \\ \\ \sf \mapsto PQ = \sqrt{4} \\ \\ \sf \mapsto PQ = 2 \: \: units$

And

$\sf \mapsto QR = \sqrt{ {(2 - 2)}^{2} + {(7 - 2)}^{2} } \\ \\ \sf \mapsto QR = \sqrt{25} \\ \\ \sf \mapsto QR = 5 \: \: units$

And

$\sf \mapsto PR = \sqrt{ {(2 - ( - 2))}^{2} + {(7 - 2)}^{2} } \\ \\ \sf \mapsto PR = \sqrt{ 4 + 25} \\ \\ \sf \mapsto PR = \sqrt{29} \: \: units$

It is observed that ,

(PR)² = (QR)² + (PQ)²

$\sf \therefore \underline{The \: given \: triangle \: is \: right \: angled \: triangle }$

Answer 2

Answer:

Bajaj

nak

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Step-by-step explanation:

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