Question

coordinate distance (decimal)
score: 1/2
question
find the distance between the two points rounding to the nearest tenth (if necessary).
(4,1) and (-2,9)
answer
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Explanation:

Step1: Recall the distance formula

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Step2: Identify the coordinates

Let \((x_1, y_1) = (4, 1)\) and \((x_2, y_2) = (-2, 9)\).

Step3: Substitute into the formula

First, calculate the differences: \(x_2 - x_1 = -2 - 4 = -6\) and \(y_2 - y_1 = 9 - 1 = 8\).
Then, square these differences: \((-6)^2 = 36\) and \(8^2 = 64\).
Add the squared differences: \(36 + 64 = 100\).
Take the square root: \(d = \sqrt{100} = 10.0\) (since \(\sqrt{100}=10\), and to the nearest tenth, it's \(10.0\)).

Answer:

10.0