Answer:
The length of the segment = 8.1 units
Explanations:
The length of the segments with endpoints (x₁, y₁) and (x₂, y₂) is given by the equation:
![D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/blvd5bizpfsp1rctvjgv7h5pscu3lv9ga5.png)
If the endpoints are (3,-2) and (-1,5):
x₁ = 3, y₁ = -2, x₂ = -1, y₂ = 5
Substituting these coordinates into the formula above:
![\begin{gathered} D\text{ = }\sqrt[]{(-1-3)^2+(5-(-2))^2} \\ D\text{ = }\sqrt[]{(-4)^2+(7)^2} \\ D\text{ = }\sqrt[]{16+49} \\ D\text{ = }\sqrt[]{65} \\ D\text{ = }8.1 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/scug75zw5fz7rancm7wmmekiyqnnba9s0y.png)
The length of the segment = 8.1 units