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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 ______.
Options
– 4
– 12
- 12
12
– 6
Solution
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.
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