To find the coordinates of point [tex]\(L\)[/tex], the midpoint of [tex]\(\overline{JK}\)[/tex], you can use the midpoint formula. The midpoint formula calculates the average of the x-coordinates and the y-coordinates of the endpoints of a line segment.
Given two points [tex]\(J(x_1, y_1)\)[/tex] and [tex]\(K(x_2, y_2)\)[/tex], the formula for the midpoint [tex]\(M(x_M, y_M)\)[/tex] is:
[tex]\[M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)\][/tex]
Here, the coordinates of point [tex]\(J\)[/tex] are [tex]\( (5, 3) \)[/tex], and the coordinates of point [tex]\(K\)[/tex] are [tex]\( (1, -7) \)[/tex].
Let's apply the midpoint formula step by step:
1. Calculate the x-coordinate of the midpoint:
[tex]\[ M_x = \frac{x_1 + x_2}{2} = \frac{5 + 1}{2} = \frac{6}{2} = 3.0 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ M_y = \frac{y_1 + y_2}{2} = \frac{3 + (-7)}{2} = \frac{3 - 7}{2} = \frac{-4}{2} = -2.0 \][/tex]
So, the coordinates of point [tex]\(L\)[/tex] are [tex]\((3.0, -2.0)\)[/tex].
Thus, the answer is:
[tex]\[ L(3, -2) \][/tex]
