Answer:
[tex]\sqrt{221}[/tex]
Step-by-step explanation:
The distance formula is:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
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.
[tex]d = \sqrt{(8 - (-6))^2 + (-2-3)^2}[/tex]
First, solve inside the parentheses
[tex]d = \sqrt{(8+6)^2 + (-2-3)^2}[/tex]
[tex]d = \sqrt{(14)^2 + (-5)^2}[/tex]
Solve the exponents.
14^2=14*14=196
[tex]d=\sqrt{196+(-5)^2}[/tex]
-5^2=-5*-5=25
[tex]d=\sqrt{196+25}[/tex]
Add 196 and 25
[tex]d=\sqrt{221}[/tex]
d=14.8660687473
The distance between the points is [tex]\sqrt{221}[/tex] or about 14.87
