Answer:
C) 10.63 units.
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
We have the two points (2, -3) and (-6, 4). Let (2, -3) be (<em>x₁, y₁</em>) and let (-6, 4) be (<em>x₂, y₂</em>). Substitute:
![d=\sqrt{(-6-2)^2+(4-(-3))^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-6-2%29%5E2%2B%284-%28-3%29%29%5E2%7D)
Simplify:
![d=\sqrt{(-8)^2+(7)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-8%29%5E2%2B%287%29%5E2%7D)
Evaluate:
![d=\sqrt{64+49}=\sqrt{113}\approx10.63\text{ units}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B64%2B49%7D%3D%5Csqrt%7B113%7D%5Capprox10.63%5Ctext%7B%20units%7D)
Our answer is C.