Question

If `P(a/3, 4)` is the mid-point of the line segment joining the points Q(– 6, 5) and R(– 2, 3), then the value of a is ______.

पर्याय

• – 4

• – 12

• - 12

• 12

• – 6

Answer 1

If `P(a/3, 4)` is the mid-point of the line segment joining the points Q(– 6, 5) and R(– 2, 3), then the value of a is – 12.

Explanation:

Given that, `P(a/3, 4)` 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:

∴ Mid-point of QR = `P((-6 - 2)/2, (5 + 3)/2)` = P(– 4, 4)  ...`["Since, mid-point of line segment having points"  (x_1, y_1)  "and"  (x_2, y_2) = (((x_1 + x_2))/2, ((y_1 + y_2))/2)]`

But mid-point `P(a/3, 4)` is given.

∴ `(a/3, 4)` = (– 4, 4)

On comparing the coordinates, we get

`a/3` = – 4

∴ a = – 12

Hence, the required value of a is – 12.