A) equilateral
B) right angle
C) isosceles
D) None of these
Correct Answer: C
Solution :
| Let \[P\left( 5,\,-2 \right),\,Q\left( 6,\,4 \right)\] and \[R\left( 7,\,-2 \right)\] |
| are the given points. Then, \[PQ=\sqrt{{{\left( 6-5 \right)}^{2}}+{{\left( 4+2 \right)}^{2}}}\] |
| \[\left[ \because \,d=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}} \right]\] |
| \[=\sqrt{1+36}=\sqrt{37}\] units |
| \[QR=\sqrt{{{\left( 7-6 \right)}^{2}}+{{\left( -2-4 \right)}^{2}}}\] |
| \[=\sqrt{1+36}=\sqrt{37}\] units |
| Since, \[PQ=QR\] |
| \[\therefore \,\,\,\Delta PQR\] is an isosceles triangle. |
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