Find the distance between (2, 3) and (-4, -9). Round your answer to the nearest hundredth, if necessary.
The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula
$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.$
For $(2,3)$ and $(-4,-9),$ this is $\sqrt{(-4 - 2)^2 + (-9 - 3)^2} = \sqrt{36 + 144} = \sqrt{180} = \boxed{13.42}.$
To find the distance between two points in a coordinate plane, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's plug in the given coordinates (x1, y1) = (2, 3) and (x2, y2) = (-4, -9) into the formula:
d = sqrt((-4 - 2)^2 + (-9 - 3)^2)
Simplifying,
d = sqrt((-6)^2 + (-12)^2)
= sqrt(36 + 144)
= sqrt(180)
To round the answer to the nearest hundredth, we can use a calculator or approximations:
sqrt(180) ≈ 13.42
Therefore, the distance between the points (2, 3) and (-4, -9) is approximately 13.42 units.
To find the distance between two points, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance between (2, 3) and (-4, -9) using this formula:
distance = sqrt((-4 - 2)^2 + (-9 - 3)^2)
= sqrt((-6)^2 + (-12)^2)
= sqrt(36 + 144)
= sqrt(180)
≈ 13.42
Therefore, the distance between (2, 3) and (-4, -9) is approximately 13.42 units when rounded to the nearest hundredth.