A) -4
B) -12
C) 12
D) -6
Correct Answer: B
Solution :
Given that, \[P\left( \frac{a}{3},\,4 \right)\]is the mid-point of the line segment joining the points Q (-6, 5) and R (-2, 3), which shows in the figure given below |
\[\therefore\] Mid-point of \[QR=P\left( \frac{-6-2}{2},\,\frac{5+3}{2} \right)\] |
=P(-4,4) |
[since, mid-point of line segment having points \[\left( {{x}_{1}},\,{{y}_{1}} \right)\] and \[\left( {{x}_{2}},\,{{y}_{2}} \right)\] |
\[\left. =\left( \frac{\left( {{x}_{1}}+{{x}_{2}} \right)}{2},\frac{\left( {{y}_{1}}+{{y}_{2}} \right)}{2} \right) \right]\] |
But mid-point \[P\left( \frac{a}{3},\,4 \right)\] is given. |
\[\therefore \,\,\,\left( \frac{a}{3},\,4 \right)=\left( -4,\,\,4 \right)\] |
On comparing the coordinates, we get |
\[\frac{a}{3}=-4\] |
\[\Rightarrow \,\,\,a=-12\] |
Hence, the required value of a is -12. |
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