1. **State the problem:** Find the midpoint of the line segment connecting the points (-2, 3) and (0, 6). 2. **Formula for midpoint:** The midpoint $M$ of a segment with endpoints $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by: $$M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$ This means we take the average of the x-coordinates and the average of the y-coordinates. 3. **Apply the formula:** $$M=\left(\frac{-2+0}{2},\frac{3+6}{2}\right)$$ 4. **Simplify the sums:** $$M=\left(\frac{-2}{2},\frac{9}{2}\right)$$ 5. **Simplify the fractions:** $$M=\left(-1,\frac{9}{2}\right)$$ 6. **Interpretation:** The midpoint is at $(-1, \frac{9}{2})$, which means it is 1 unit left of the origin and 4.5 units up. --- 1. **State the problem:** Find the midpoint of the line segment connecting (-5, -1) and (1, 3). 2. **Apply the formula:** $$M=\left(\frac{-5+1}{2},\frac{-1+3}{2}\right)$$ 3. **Simplify the sums:** $$M=\left(\frac{-4}{2},\frac{2}{2}\right)$$ 4. **Simplify the fractions:** $$M=\left(-2,1\right)$$ --- 1. **State the problem:** Find the midpoint of the line segment connecting (-6, 2) and (2, -4). 2. **Apply the formula:** $$M=\left(\frac{-6+2}{2},\frac{2+(-4)}{2}\right)$$ 3. **Simplify the sums:** $$M=\left(\frac{-4}{2},\frac{-2}{2}\right)$$ 4. **Simplify the fractions:** $$M=\left(-2,-1\right)$$ --- **Final answers:** 1. Midpoint = $(-1,\frac{9}{2})$ 2. Midpoint = $(-2,1)$ 3. Midpoint = $(-2,-1)$