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

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 (xy) be the mid point of AB. Then:

$x=\frac{x_{1}+x_{2}}{2}, y=\frac{y_{1}+y_{2}}{2}$

$\Rightarrow x=\frac{6+(-2)}{2}, y=\frac{-5+11}{2}$

$\Rightarrow x=\frac{6-2}{2}, y=\frac{-5+11}{2}$

$\Rightarrow x=\frac{4}{2}, y=\frac{6}{2}$

$\Rightarrow x=2, y=3$

So, the midpoint of AB is (2, 3).
But it is given that the midpoint of AB is (2, p).
Therefore, the value of p = 3.

 

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