Answer:
The length of the segment = 7.2 units
Explanations:
The distance between two points of coordinates (x₁, y₁) and (x₂, y₂) is given by the equation:
![L\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/sdnwfas4ik6bc6avt365kz861ny25ftmsy.png)
To find the length of the segment with endpoints (2, -1) and (-4, 3),
substitute x₁ = 2, y₁ = -1, x₂ = -4, y₂ = 3 into the equation above:
![\begin{gathered} L\text{ = }\sqrt[]{(-4-2)^2+(3-(-1))^2} \\ L\text{ = }\sqrt[]{(-6)^2+(4)^2} \\ L\text{ = }\sqrt[]{36+16} \\ L\text{ = }\sqrt[]{52} \\ L\text{ = }7.2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/kqn5yrtlbq9jaydkol1f0ghtfxls4s5l8q.png)
The length of the segment = 7.2 units