Answer:
[tex]distance=\sqrt{(-2-(-5))^{2} +(6-(-10))^{2}}[/tex]
distance = 16.2788
Step-by-step explanation:
This question is asking you to correctly apply the distance formula. This formula determines the straight line distance between two points by applying Pythagorean's Theorem ([tex]h = \sqrt{x^{2}+y^{2} }[/tex]). The distance formula can be thought of as [tex]distance=\sqrt{(x_{1}-x_{2})^{2} +(y_{1}-y_{2})^{2}}[/tex]. It doesn't matter which order you put your coordinates into the equation as long as it's the square root of the change in x-coordinates squared + change in y-coordinates squared.
Step 1: change in x-coordinates
x1 = -2
x2 = -5
x1 - x2 = -2 - (-5) = 3
Step 2: change in y-coordinates
y1 = 6
y2 = -10
y1 - y2 = 6 - (-10) = 16
Step 3: plug into distance formula
[tex]distance=\sqrt{(-2-(-5))^{2} +(6-(-10))^{2}}[/tex]
[tex]distance=\sqrt{(3)^{2} +(16)^{2}}[/tex]
[tex]distance=\sqrt{9 +256}[/tex]
[tex]distance=\sqrt{265}[/tex]
distance = 16.2788
