Answer:
![\sqrt{221}](https://tex.z-dn.net/?f=%5Csqrt%7B221%7D)
Step-by-step explanation:
The distance formula is:
![d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2-y_1%29%5E2%7D)
where (x1, y1) are the coordinates of the first point, and (x2,y2) are the coordinates of the second point.
The point X is at (-6,3). The point Y is at (8, -2). Therefore, we can plug these points into the formula.
![d = \sqrt{(8 - (-6))^2 + (-2-3)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%288%20-%20%28-6%29%29%5E2%20%2B%20%28-2-3%29%5E2%7D)
First, solve inside the parentheses
![d = \sqrt{(8+6)^2 + (-2-3)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%288%2B6%29%5E2%20%2B%20%28-2-3%29%5E2%7D)
![d = \sqrt{(14)^2 + (-5)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%2814%29%5E2%20%2B%20%28-5%29%5E2%7D)
Solve the exponents.
14^2=14*14=196
![d=\sqrt{196+(-5)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B196%2B%28-5%29%5E2%7D)
-5^2=-5*-5=25
![d=\sqrt{196+25}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B196%2B25%7D)
Add 196 and 25
![d=\sqrt{221}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B221%7D)
d=14.8660687473
The distance between the points is
or about 14.87