Question

if p(a/3.4) is the mid-point of the line Segment joining the points & q(-6,5) and R (-2,3), then.
what is the value of a​

Answer 1

Step-by-step explanation:

P is the mid - point of the line segment joining the points Q and R

Where;

P = (a/3, 4)

Q = ( - 6, 5)

R = ( - 2, 3)

Shown in the figure given below;

∴ a = - 12

Hence, the required value of a = - 12

Answer 2

Step-by-step explanation:

Given:-

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

To find:-

what is the value of a ?

Solution:-

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

Let ( x1 ,y1) = Q(-6,5)=>x1 = -6 and y1 = 5

Let (x2, y2)=R(-2,3)=>x2 = -2 and y2 = 3

We know that

The mid point of a line segment joining the points (x1, y1) and (x2, y2) is [(x1+x2)/2, (y1+y2)/2]

Now mid point of the line segments joining the points Q and R

=>[(-6+(-2))/2,(5+3)/2]

=>(-6-2)/2,8/2))

=>(-8/2,8/2)

=>(-4,4)

According to the given problem

Mid point of the line segment joining the points Q and R = P(a/3,4)

=>(a/3,4) = (-4,4)

On Comparing both sides then

=>a/3 = -4

=>a = -4×3

=>a = -12

Therefore, a = -12

Answer:-

The value of a for the given problem is -12

Used formula:-

The mid point of a line segment joining the points (x1, y1) and (x2, y2) is [(x1+x2)/2, (y1+y2)/2]