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
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Answer 1

Answer:

Explanation:

Given :

• Point P is the midpoint of seg AB.
• P(a/2 , 4) , A(-6 , 5) & B(-2 , 3).

To Find :

• The value of a.

Solution :

Given, P(a/2 , 4) , A(-6 , 5) & B(-2 , 3).

Here,

• x = a/2
• y = 4
• x1 = -6
• y1 = 5
• x2 = -2
• y2 = 3

Given that, Point P is the midpoint of seg AB.

Applying midpoint formula,

x = x1 + x2/2 & y = y1 + y2/2

We need to find the value of a, So ;

• x = x1 + x2/2

=> a/2 = -6 + (-2)/2

=> a/2 = -6 - 2/2

=> a/2 = -8/2

=> a/2 = -4

=> a = -4 × 2

=> a = -8

Hence :

The value of a is -8.

Answer 2

Given : $\sf \: P\left(\dfrac{a}{2},4\right)\: is \: the \: midpoint \: of \: segment \: AB \: joining \: the \: points \: A(-6 , 5) \: and \: B(-2 , 3).$

To Find : $\sf \: Value \: of \: a.$⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀__________________

Here

• $\:$$\sf \: (x1 , y1 ) = \: (-6 , 5)$
• $\sf \: (x , y) = \left(\dfrac{a}{2},4\right)$
• $\sf \: (x2 , y2) = (-2 , 3)$

$\: \:$

★ A P P L Y ⠀ M I D P O I N T ⠀ F O R M U L A :

$\: \:$

$\: \:$

⠀$\bigstar\underline{\boxed{\sf\purple{{\left( x = \frac{x1 + x2}{2} \right)}}}}$

$\:$

$\:$$\sf:\implies \: \dfrac{a}{2} = \left( \dfrac{ - 6 + ( - 2)}{2} \right)$

$\:$

$\sf:\implies \: \dfrac{a}{2} = \left( \dfrac{ - 6 - 2}{2} \right)$

$\:$

$\sf:\implies \: \dfrac{a}{2} = \cancel \dfrac{ - 8}{2}$

$\:$

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

$\:$

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

$\:$

$\sf:\implies \: a = \underline{\boxed{\sf\purple{ - 8}}}\bigstar$

$\: \:$

$\: \:$

$\sf\therefore{\underline{Hence, \: the \: value \: of \: a \: is \: \bold{ - 8}.}}$