KCET · Maths · Straight Lines
The line joining \(A(2,-7)\) and \(B(6,5)\) is divided into 4 equal parts by the points \(\mathrm{P}, \mathrm{Q}\) and \(\mathrm{R}\) such that \(\mathrm{AQ}=\mathrm{RP}=\mathrm{QB}\). The mid point of \(P R\) is
- A \((4,12)\)
- B \((-8,1)\)
- C \((4,-1)\)
- D \((8,-2)\)
Answer & Solution
Correct Answer
(C) \((4,-1)\)
Step-by-step Solution
Detailed explanation
Given that,
\[
\text { and } \quad \begin{aligned}
\mathrm{AP} &=\mathrm{PQ}=\mathrm{QR}=\mathrm{RB} \\
\mathrm{AQ} &=\mathrm{RP}=\mathrm{QB}
\end{aligned}
\]
Since, \(\mathrm{AQ}=\mathrm{QB}\), that means \(\mathrm{Q}\) is the mid point of \(\mathrm{AB}=\left[\frac{2+6}{2}, \frac{-7+5}{2}\right]=(4,-1)\)
\(\because\) Mid point of \(P R=(4,-1)\)
\([\because \mathrm{PQ}=\mathrm{QR}]\)
\[
\text { and } \quad \begin{aligned}
\mathrm{AP} &=\mathrm{PQ}=\mathrm{QR}=\mathrm{RB} \\
\mathrm{AQ} &=\mathrm{RP}=\mathrm{QB}
\end{aligned}
\]
Since, \(\mathrm{AQ}=\mathrm{QB}\), that means \(\mathrm{Q}\) is the mid point of \(\mathrm{AB}=\left[\frac{2+6}{2}, \frac{-7+5}{2}\right]=(4,-1)\)
\(\because\) Mid point of \(P R=(4,-1)\)
\([\because \mathrm{PQ}=\mathrm{QR}]\)
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