The problem asks to find the distance between the points $(-2, 2)$ and $(-8, 10)$. The answer should be rounded to the nearest tenth.

GeometryDistance FormulaCoordinate GeometryPointsEuclidean Distance
2025/3/13

1. Problem Description

The problem asks to find the distance between the points (2,2)(-2, 2) and (8,10)(-8, 10). The answer should be rounded to the nearest tenth.

2. Solution Steps

To find the distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), we use the distance formula:
d=(x2x1)2+(y2y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
In this case, (x1,y1)=(2,2)(x_1, y_1) = (-2, 2) and (x2,y2)=(8,10)(x_2, y_2) = (-8, 10).
Plugging these values into the distance formula, we get:
d=(8(2))2+(102)2d = \sqrt{(-8 - (-2))^2 + (10 - 2)^2}
d=(8+2)2+(8)2d = \sqrt{(-8 + 2)^2 + (8)^2}
d=(6)2+(8)2d = \sqrt{(-6)^2 + (8)^2}
d=36+64d = \sqrt{36 + 64}
d=100d = \sqrt{100}
d=10d = 10

3. Final Answer

10.0

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