If M(4, 5) is the mid-point of the line segment joining the points A(k, 4) and B(7, -3 p), then find the value of 2k + 3p.

-4

Midpoints of two points with coordinates (x1 , y1) & (x2, y2)  is (x , y ) :-

( x , y ) = ( \(\frac{x1 + x2 }{2}\) , \(\frac{y1 + y2 }{2}\) )

( 4  , 5 ) = ( \(\frac{k + 7 }{2}\) , \(\frac{4 -3p }{2}\) )

\(\frac{k + 7 }{2}\) = 4  ,  \(\frac{4 -3p }{2}\) = 5

k = 1 , - 3p = 6

k = 1 , p = -2

Now , 2k + 3p = 2 × 1 + 3 ( - 2 )

= 2 - 6

= - 4

The correct answer is Option (1) → -4