Questions: Find the midpoint of the line segment joining points A and B. A(2,-5) ; B(4,1) The midpoint of the line segment is . (Type an ordered pair.)

Solution Steps

To find the midpoint of a line segment joining two points $A(x_1, y_1)$ and $B(x_2, y_2)$, we use the midpoint formula: $$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ Given points $A(2, -5)$ and $B(4, 1)$, we substitute these values into the formula to find the midpoint.

We are given two points $A(2, -5)$ and $B(4, 1)$.

To find the midpoint $M$ of the line segment joining points $A$ and $B$, we use the midpoint formula: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ Substituting the coordinates of points $A$ and $B$: $$M = \left( \frac{2 + 4}{2}, \frac{-5 + 1}{2} \right)$$

Calculating the x-coordinate: $$\frac{2 + 4}{2} = \frac{6}{2} = 3.0$$ Calculating the y-coordinate: $$\frac{-5 + 1}{2} = \frac{-4}{2} = -2.0$$ Thus, the midpoint $M$ is $(3.0, -2.0)$.

Final Answer