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Mathematics

Assertion (A) : If (3a, 4) is the mid-point of the line segment joining points (-6, 5) and (-2, 3); then a = -4.

Reason (R) : The mid-point of the line segment joining the points (x1, y1) and (x2, y2) is (x1+x22,y1+y22)\Big(\dfrac{x1+ x2}{2}, \dfrac{y1 + y2}{2}\Big).

  1. A is true, R is false.

  2. A is false, R is true.

  3. Both A and R are true.

  4. Both A and R are false.

Section Formula

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Answer

By mid-point formula,

Mid-point (M) = (x1+x22,y1+y22)\Big(\dfrac{x1+ x2}{2}, \dfrac{y1 + y2}{2}\Big).

Given,

(3a, 4) is the mid-point of the line segment joining points (-6, 5) and (-2, 3).

(3a,4)=(6+(2)2,5+32)(3a,4)=(82,82)(3a,4)=(4,4)3a=4a=43.\therefore (3a, 4) = \Big(\dfrac{-6 + (-2)}{2}, \dfrac{5 + 3}{2}\Big) \\[1em] \Rightarrow (3a, 4) = \Big(\dfrac{-8}{2}, \dfrac{8}{2}\Big) \\[1em] \Rightarrow (3a, 4) = (-4, 4) \\[1em] \Rightarrow 3a = -4 \\[1em] \Rightarrow a = -\dfrac{4}{3}.

∴ Assertion (A) is false and Reason (R) is true.

Hence, Option 2 is the correct option.

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