Question: DF \parallel BC
ED \parallel BA
AB \parallel EF
Graph shape: a quadrilateral-like line figure with vertices A, D, top vertex, E, C, and F connected by segments; A-D-top-E-C forms the outer boundary, with A-F-C also on the lower boundary, and interior segments D-F, D-E, and F-E. position_hint: center
What are the coordinates for the midpoint of NM?
Enter your answer like (1,2) with no spaces
1 (3,4)
Graph: coordinate plane with x-axis horizontal and y-axis vertical; point N is at (0,2), point L is at (0,5), and point M is at (6,4). Two line segments connect L to M and N to M, forming a triangle-like shape. position_hint=center
User: Solve
1. **State the problem:** Find the coordinates of the midpoint of segment $NM$ where $N=(0,2)$ and $M=(6,4)$.
2. **Formula for midpoint:** The midpoint $P$ of a segment with endpoints $A=(x_1,y_1)$ and $B=(x_2,y_2)$ is given by:
$$P=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$
3. **Apply the formula:**
$$P=\left(\frac{0+6}{2},\frac{2+4}{2}\right)$$
4. **Simplify the coordinates:**
$$P=\left(\frac{6}{2},\frac{6}{2}\right)$$
5. **Cancel common factors:**
$$P=\left(\cancel{\frac{6}{2}},\cancel{\frac{6}{2}}\right) = (3,3)$$
6. **Final answer:** The midpoint of $NM$ is at coordinates $(3,3)$.