Answer:
The coordinates of the midpoint are [tex]M(x,y) = \left(7, \frac{15}{2} \right)[/tex], respectively.
Explanation:
Given two distinct points ([tex]A(x,y)[/tex], [tex]B(x,y)[/tex]), the midpoint of the segment ([tex]M(x,y)[/tex]) is determined by the following expression:
[tex]M(x,y) = \frac{1}{2}\cdot A(x,y) + \frac{1}{2}\cdot B(x,y)[/tex] (1)
If we know that [tex]A(x,y) = (10, 6)[/tex] and [tex]B(x,y) = (4,9)[/tex], then the coordinates of the midpoint are:
[tex]M(x,y) = \frac{1}{2}\cdot (10, 6) + \frac{1}{2}\cdot (4,9)[/tex]
[tex]M(x,y) = (5,3) + \left(2,\frac{9}{2} \right)[/tex]
[tex]M(x,y) = \left(7, \frac{15}{2} \right)[/tex]
The coordinates of the midpoint are [tex]M(x,y) = \left(7, \frac{15}{2} \right)[/tex], respectively.
