Question

Find the co-ordinates of the midpoint of the line segment joining the points A (6,- 2) and B ( - 2,8).​

Answer 1

$\huge { \red { \fbox{ \fcolorbox{blue}{green}{ \bf \purple{(2,3)}}}}}$

Step-by-step explanation:

Given :-

• Point A(6 , - 2)
• Point B(- 2 , 8)

.

To find :-

• The midpoint of the line segment joining the given points.

SOLUTION :-

Here,

$\bf( x_{1}, y_{1}) = (6, - 2) \\ \bf x_{1} = 6, y_{1} = - 2 \\ \\ \bf (x_{2}, y_{2}) = ( - 2,8) \\ \bf x_{2} = - 2, y_{2} = 8$

Now,

using the midpoint formula, we will find the midpoint p(x,y) -

Midpoint formula -

$\bf p(x,y) = ( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2} }{2} ) \\ \\ \bf= ( \frac{6 + ( - 2)}{2} , \frac{ - 2 + 8}{2} ) \\ \\ \bf = (\frac{6 -2 }{2} , \frac{8 - 2}{2} ) \\ \\ \bf = ( \frac{4}{2} , \frac{6}{2} ) \\ \\ \bf = (2,3)$

So,

the midpoint of the line segment is (2 , 3).

Hope it helps.