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  • 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 (A) – 4 (B) – 12 (C) 12 (D) – 6

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

(A) – 4

(B) – 12

(C) 12

(D) – 6

Answers (1)

\\ \mathrm{Q}(-6,5) \quad \mathrm{R}(-2,3)\\\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \quad\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)

By using mid-point formula

\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)  
P=\left(\frac{-6-2}{2}, \frac{5+3}{2}\right)
\\ \left(\frac{a}{3}, 4\right)=\left(\frac{-8}{2}, \frac{8}{2}\right) \\\left(\frac{a}{3}, 4\right)=(-4,4)
Compare x co-ordinate
\\\frac{a}{3}=-4$ \\$a=-4 \times 3$ \\$a=-12

Hence, option B is correct.

Posted by

infoexpert21

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