Find the distance between (2, 3) and (−4, −9) . Round your answer to the nearest hundredth, if necessary.
I apologize for the mistake. Let me redo the calculation correctly:
To find the distance between two points (2, 3) and (-4, -9), we can use the distance formula:
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
Plugging in the values from the given points, we have:
\[d = \sqrt{((-4) - 2)^2 + ((-9) - 3)^2} = \sqrt{(-6)^2 + (-12)^2} = \sqrt{36 + 144} = \sqrt{180}\]
Rounded to the nearest hundredth, the distance between the two points is approximately 13.42.
To find the distance between two points, we can use the distance formula:
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
Plugging in the values from the given points, we have:
\[d = \sqrt{((-4) - 2)^2 + ((-9) - 3)^2} = \sqrt{(-6)^2 + (-12)^2} = \sqrt{36 + 144} = \sqrt{180}\]
Rounding to the nearest hundredth, we have:
\[d \approx \sqrt{180} \approx 13.42\]
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To find the distance between two points in a coordinate plane, you can use the distance formula. The distance formula is derived from the Pythagorean theorem.
The formula to find the distance between two points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance between the points (2, 3) and (-4, -9) using this formula:
Let (x1, y1) = (2, 3) and (x2, y2) = (-4, -9)
Substituting the values into the formula, we get:
d = √((-4 - 2)^2 + (-9 - 3)^2)
Simplifying further:
d = √((-6)^2 + (-12)^2)
d = √(36 + 144)
d = √180
To round the answer to the nearest hundredth, we need to find the square root of 180. Using a calculator, we find:
√180 ≈ 13.42
Therefore, the distance between the points (2, 3) and (-4, -9) is approximately 13.42 units when rounded to the nearest hundredth.