Question

P(a/2 ,4) is the midpoint of seg AB joining the points A(-6,5) and B(-2,3).
Find the value of a.

Answer 1

❍ Let the given points be P(2/3, 4) is the mid point of line segment AB joining points A(-6, 5) and B(-2,3).

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$\therefore$ Co-ordinates of point P.

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$:\implies\sf P = \bigg(\dfrac{-6 +2}{2} \bigg) , \bigg(\dfrac{5 + 3}{2} \bigg) \\\\\\:\implies\sf P = \bigg(\dfrac{-8}{2} , \dfrac{8}{2} \bigg) \\\\\\:\implies\sf \Big(-4, 4 \Big)$

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It is given that,

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$:\implies\sf P = \Bigg(\dfrac{a}{2}, 4 \Bigg)$

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Therefore,

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$:\implies\sf \dfrac{a}{2} = -4\\\\\\:\implies\sf a = -4 \times 2 \\\\\\:\implies{\underline{\boxed{\frak{\purple{a = -8}}}}}\:\bigstar$

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⠀⠀$\therefore\:{\underline{\sf{Hence, \ required \: value \: of \: 'a' \: is \: \bf{-8}.}}}$⠀⠀

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$\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: Additional \: Information\: : }}}}}\mid}$

• To find out the distance b/w two given points the formula is, $\sf D = \sqrt{\Big(x_2 - x_1 \Big)^2 + \Big(y_2 - y_1 \Big)^2}$⠀

Answer 2

Answer:

Required Answer :-

Let us assume P(2/3, 4) is the mid point of line segment AB joining points A(-6, 5) and B(-2,3).

Now

Co-ordinate of P :-

$\sf P \: = \bigg( \dfrac{ - 6 + 2}{2} \bigg), \bigg ( \dfrac{5 + 3}{2} \bigg)$

$\sf \: P\: = \bigg( \dfrac{ - 8}{2} \bigg), \bigg( \dfrac{8}{2} \bigg)$

$\sf \: P\: = - 4,4$

Now,

$\sf \: P \: = \dfrac{a}{2} - 4$

$\sf \dfrac{a}{2} = - 4$

$\sf \: a \: = - 4 \times 2$

$\bf \pink{a = - 8}$