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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Mathematics
Chapter
Straight Lines

BITSAT 2021 · Mathematics · Straight Lines

The points (0,7,10),(-1,6,6) and (-4,9,6) form

The points (0,7,10),(−1,6,6)(0,7,10),(-1,6,6) and (−4,9,6)(-4,9,6) form

Options

  1. Aa right angled isosceles triangle
  2. Ba scalene triangle
  3. Ca right angled triangle
  4. Dan equilateral triangle

Correct answer

A. a right angled isosceles triangle

Step-by-step solution

Let P(0,7,10),Q(−1,6,6)\mathrm{P}(0,7,10), \mathrm{Q}(-1,6,6) and R(−4,9,6)\mathrm{R}(-4,9,6) be the vertices of a triangle Here, PQ=1+1+16=32\mathrm{PQ}=\sqrt{1+1+16}=3 \sqrt{2}QR=9+9+0=32PR=16+4+16=6 Now, PQ2+QR2=(32)2+(32)2=36=(PR)2\begin{array}{l} \mathrm{QR}=\sqrt{9+9+0}=3 \sqrt{2} \\ \mathrm{PR}=\sqrt{16+4+16}=6 \\ \text{ Now, } \mathrm{PQ}^{2}+\mathrm{QR}^{2}=(3 \sqrt{2})^{2}+(3 \sqrt{2})^{2}=36=(\mathrm{PR})^{2} \end{array}Therefore,Therefore,\triangle PQR\mathrm{PQR} is a right angled triangle at Q\mathrm{Q}. Also, OQ=QR\mathrm{OQ}=\mathrm{QR}. Hence, △PQRisarightangledisoscelestriangle.\triangle \mathrm{PQR} is a right angled isosceles triangle.
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