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Mathematics

If P(a3,4)P(\dfrac{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

  1. -4

  2. -6

  3. 12

  4. -12

Section Formula

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Answer

We know that,

Mid-point formula = ((x1+x2)2,(y1+y2)2)\Big(\dfrac{(x1 + x2)}{2}, \dfrac{(y1 + y2)}{2}\Big)

Given, P is the midpoint of line segment QR. Putting the values in mid-point formula for x-coordinate we get,

⇒a3=−6+(−2)2⇒a=−82×3⇒a=−4×3⇒a=−12.\Rightarrow \dfrac{a}{3} = \dfrac{-6 + (-2)}{2} \\[1em] \Rightarrow a = \dfrac{-8}{2} \times 3 \\[1em] \Rightarrow a = -4 \times 3 \\[1em] \Rightarrow a = -12.

Hence, Option 4 is the correct option.

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