Given,

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

Where;

P =

Q = ( - 6, 5)

R = ( - 2, 3)

Shown in the figure given below;

∴ Mid - point of QR = P

P = ( - 4, 4)

Since, mid - point of line segment having points (x₁, y₁) and (x₂, y₂);

=

But given coordinates of mid - point P is ;

∴ ( - 4, 4)

On comparing the coordinates, we get

= - 4

∴ a = - 12

Hence, the required value of a = - 12