Question

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

then find the value of'a'.

Answer 1

The value of a = -12.

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}` ,
`( y_(1) + y_(2) )/(2)` )

Here,

Q( -6, 5) and R ( -2, 3)

then the midpoints C are-

( a/3, 4) = (
`(- 6 + ( - 2))/(2)`,
`( 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

a = -12

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