Answer this question by plugging each coordinate point into the distance formula, which is used to calculate the distance between two points.
The distance formula is:
[tex] \text{ Distance } = \sqrt{(x_2 -x_1)^2 + (y_2- y_1)^2}
[/tex]
where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are your coordinate points.
One of your coordinate points must be (-6, -10), let's make that our [tex](x_1, y_1)[/tex]. The other coordinate point is one of your answer choices.
Let's test each one:
Choice A (-3, -2):
[tex]\text{ Distance } = \sqrt{(x_2 -x_1)^2 + (y_2- y_1)^2}\\
= \sqrt{((-3) -(-6))^2 + ((-2)- (-10))^2} \\
= \sqrt{(3)^2 + (8)^2}\\
= \sqrt{9 + 64}\\
= \sqrt{73} [/tex]
This is not the right distance.
Choice B (3, 2):
[tex]\text{ Distance } = \sqrt{(x_2 -x_1)^2 + (y_2- y_1)^2}\\
= \sqrt{((3) -(-6))^2 + ((2)- (-10))^2} \\
= \sqrt{(9)^2 + (12)^2}\\
= \sqrt{81 + 144}\\
= \sqrt{225} \\
= 15[/tex]
This is the right distance!
Choice C (2, 3):
[tex]\text{ Distance } = \sqrt{(x_2 -x_1)^2 + (y_2- y_1)^2}\\
= \sqrt{((2) -(-6))^2 + ((3)- (-10))^2} \\
= \sqrt{(8)^2 + (13)^2}\\
= \sqrt{64 + 169}\\
= \sqrt{233} [/tex]
This is not the right distance.
Choice D (-2, -3):
[tex]\text{ Distance } = \sqrt{(x_2 -x_1)^2 + (y_2- y_1)^2}\\
= \sqrt{((-2) -(-6))^2 + ((-3)- (-10))^2} \\
= \sqrt{(4)^2 + (7)^2}\\
= \sqrt{16 + 49}\\
= \sqrt{65} [/tex]
This is not the right distance.
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Answer: B) (3, 2)
