To find the midpoint of the line segment connecting two points, you use the midpoint formula. The midpoint ([tex]\(M\)[/tex]) of a segment with endpoints ([tex]\(x_1, y_1\)[/tex]) and ([tex]\(x_2, y_2\)[/tex]) is calculated as follows:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given:
- Point [tex]\(H\)[/tex] with coordinates [tex]\((-1, 2)\)[/tex]
- Point [tex]\(K\)[/tex] with coordinates [tex]\((-7, -4)\)[/tex]
Let's substitute these values into the formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[ \text{midpoint}_x = \frac{-1 + (-7)}{2} = \frac{-1 - 7}{2} = \frac{-8}{2} = -4 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ \text{midpoint}_y = \frac{2 + (-4)}{2} = \frac{2 - 4}{2} = \frac{-2}{2} = -1 \][/tex]
So, the coordinates of the midpoint [tex]\(M\)[/tex] are:
[tex]\[ M = (-4, -1) \][/tex]
Thus, the coordinates of the midpoint of [tex]\(H(-1, 2)\)[/tex] and [tex]\(K(-7, -4)\)[/tex] are [tex]\((-4, -1)\)[/tex].
