Question

if P (a/3, 4) is the midpoint of the line segment joining the points Q (- 5, 7)and R (- 3, 1) .Find the value of a.​

Answer 1

Answer:

= -12

Step-by-step explanation:

Q(-5, 7) R(-3, 1)

P(-8/2, 8/2). \P mid point

P(-4, 4)

so, a/3 = -4

or, a = -12

Answer 2

The value of a is -12.

Explanation:

We know that the midpoint of the line joining (a,b)  and (c,d) is given by ;-

$(x,y)=(\dfrac{a+c}{2}, \dfrac{b+d}{2})$

Given : The midpoint of the line segment joining the points Q (- 5, 7)and R (- 3, 1) is $P(\dfrac{a}{3},4)$

Substitute all the values in  the formula above , we get

$(\dfrac{a}{3},4)=(\dfrac{-5+(-3)}{2}, \dfrac{7+1}{2})$

Compare x-coordinate only , we get

$\dfrac{a}{3}=\dfrac{-5+(-3)}{2}$

$\dfrac{a}{3}=\dfrac{-5-3}{2}$  [Since (+)(-)=(-)]

$\dfrac{a}{3}=\dfrac{-8}{2}$  

$\dfrac{a}{3}=-4$  

$a=3\times-4=-12$  

Hence, the value of a is -12.

# learn more :

The midpoint of the line segment joining the point(4,10) and (6,2)​

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