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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.
Solution
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.
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