Find the distance between the two points $(6, -5)$ and $(9, -1)$. Round the answer to the nearest tenth, if necessary.

GeometryDistance FormulaCoordinate GeometryEuclidean Distance
2025/3/27

1. Problem Description

Find the distance between the two points (6,5)(6, -5) and (9,1)(9, -1). Round the answer to the nearest tenth, if necessary.

2. Solution Steps

The distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the distance formula:
d=(x2x1)2+(y2y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
In this case, (x1,y1)=(6,5)(x_1, y_1) = (6, -5) and (x2,y2)=(9,1)(x_2, y_2) = (9, -1).
Plugging these values into the distance formula:
d=(96)2+(1(5))2d = \sqrt{(9 - 6)^2 + (-1 - (-5))^2}
d=(3)2+(4)2d = \sqrt{(3)^2 + (4)^2}
d=9+16d = \sqrt{9 + 16}
d=25d = \sqrt{25}
d=5d = 5
Since the answer is an integer, no rounding to the nearest tenth is needed.

3. Final Answer

5

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