Find the distance between (2, 3) and (−4, −9) . Round your answer to the nearest hundredth, if necessary.(1 point)
units
The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can calculate the distance between (2, 3) and (-4, -9):
Distance = sqrt((-4 - 2)^2 + (-9 - 3)^2)
= sqrt((-6)^2 + (-12)^2)
= sqrt(36 + 144)
= sqrt(180)
≈ 13.42 units
Therefore, the distance between (2, 3) and (-4, -9) is approximately 13.42 units.
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)
Given the points (2, 3) and (-4, -9), we can substitute these values into the distance formula:
d = sqrt((-4 - 2)^2 + (-9 - 3)^2)
Simplifying:
d = sqrt((-6)^2 + (-12)^2)
d = sqrt(36 + 144)
d = sqrt(180)
To round the answer to the nearest hundredth, we can use a calculator:
d ≈ 13.42 units
To find the distance between two points in a coordinate plane, we can use the distance formula.
The distance formula is given by:
\(\displaystyle d = \sqrt{{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}}\)
where \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\) are the coordinates of the two points.
In this case, we have:
\((x_{1}, y_{1}) = (2, 3)\) and \((x_{2}, y_{2}) = (-4, -9)\)
Substituting the values into the formula, we get:
\(\displaystyle d = \sqrt{{(-4 - 2)^2 + (-9 - 3)^2}}\)
Simplifying further, we have:
\(\displaystyle d = \sqrt{{(-6)^2 + (-12)^2}}\)
\(\displaystyle d = \sqrt{{36 + 144}}\)
\(\displaystyle d = \sqrt{{180}}\)
Now, we can find an approximate value by rounding to the nearest hundredth. For this, we can use a calculator or a math tool.
Using a calculator, we find that \(\sqrt{{180}} \approx 13.42\).
Therefore, the distance between the points (2, 3) and (-4, -9) is approximately 13.42 units.