Question

If (2, p) is the midpoint of the line segment joining the points A(6, –5) and B(–2, 11), find the value of p.

Answer 1

The given points are  A(6, -5) and B(-2,11).

Let ( x,y) be the midpoint of AB. Then,

` x = (x_1+x_2)/2 , y = (y_1 +y_2)/2`

` x = (6+(-2))/2 , y = (-5+11)/ 2`

` ⇒ x = (6-2)/2 , y = (-5+11)/2`

`⇒ x = 4/2 , y = 6/2 `

x = 2, y =3

So, the midpoint of ABis (2,3) .

But it is given that midpoint of AB is ( 2, p).

Therefore, the value of  p=3.