Question

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

Answer 1

Answer:

The value of a = -12.

Step-by-step explanation:

Given that the points are Q( -6, 5) and R ( -2, 3) -

As we know that-

If a line segment AB is with endpoints ( $x_{1}, y_{1}$ ) and  ( $x_{2}, y_{2}$ ) then the mid points C are-  

C = ( $\frac{x_{1} + x_{2} } {2}$  ,  $\frac{ y_{1} + y_{2} }{2}$  )

Here,

Q( -6, 5)  and R ( -2, 3)

then the midpoints C are-

( a/3, 4)  = (  $\frac{- 6 + ( - 2)}{2}$,  $\frac{ 5 + 3 }{2}$ )

We have to find the value of x therefore we need to compare only x coordinate -

a/3 = ( -6 - 2)/2

a/3 = -8/2

a/3 = - 4

a = -12

Hence the value of a = -12.

Answer 2

Answer:

a = -12

Step-by-step explanation:

Mid point =(x₁+ x₂/2, y₁+y₂/2)

(a/3,4)    = (-6+ [-2]/2, 5+3/2)

(a/3,4)    = (-6 -2/2, 5+3/2)

(a/3,4)    = (-8/2, 8/2)

(a/3,4)    = (-4,4)

Comparing the X- co ordinates,

a/3 = -4

a = -4 *3 = -12