10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

If (a, b) is the mid-point of the line segment joining the points A(10, -6) and B(k, 4) and a - 2b = 18, then the value of k is

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

\[a-2b=18\]

\[\therefore \,\,\,\,\,\frac{10+k}{2}-2\left( -1 \right)=18\]

\[\Rightarrow \,\,\,\,\,\frac{10+k}{2}=18-2\,\,\,\Rightarrow \,\,10+k=2\times 16\]

\[\Rightarrow \,\,\,\,k=32-10\,\,\Rightarrow \,\,k=22\]