A) 30
B) 22
C) 4
D) 40
Correct Answer: B
Solution :
Given, point (a, b) is the mid-point of the line segment joining the points A (10, - 6) and B(k, 4). |
\[\therefore \] Coordinate of mid-point of |
\[AB=\left( \frac{10+k}{2},\,\frac{-6+4}{2} \right)\] |
\[\Rightarrow \,\,\,\left( a,\,b \right)=\left( \frac{10+k}{2},\,-1 \right)\] |
Equate the x and y-coordinates both sides, we get |
\[a=\frac{10+k}{2}\] and b = - 1 |
Also, given relation is |
\[a-2b=18\] |
\[\therefore \,\,\,\,\,\frac{10+k}{2}-2\left( -1 \right)=18\] |
\[\Rightarrow \,\,\,\,\,\frac{10+k}{2}=18-2\,\,\,\Rightarrow \,\,10+k=2\times 16\] |
\[\Rightarrow \,\,\,\,k=32-10\,\,\Rightarrow \,\,k=22\] |
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