Find the distance between (2,3) and (-4,-9). Round your answer to the nearest hundredth if necessary.
To find the distance between two points, we can use the distance formula.
The distance formula is given by $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.
Using the given points $(2,3)$ and $(-4,-9)$, we can substitute the values into the distance formula:
$\sqrt{((-4)-(2))^2 + ((-9)-(3))^2}$
This simplifies to:
$\sqrt{((-6))^2 + ((-12))^2} = \sqrt{36 + 144}$
Evaluating the square root, we find:
$\sqrt{180}\approx 13.416$.
Rounded to the nearest hundredth, the distance between the two points is $\boxed{13.42}$.
To find the distance between two points in a coordinate plane, we can use the distance formula. The distance formula states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the two points are (2, 3) and (-4, -9). Let's substitute these values into the distance formula to find the distance:
d = √((-4 - 2)² + (-9 - 3)²)
Simplifying this expression, we have:
d = √((-6)² + (-12)²)
= √(36 + 144)
= √180
Now, to round the answer to the nearest hundredth, we need to find the square root of 180 and round it to two decimal places. Let's calculate this:
d ≈ √180
≈ 13.416
Rounding this to the nearest hundredth, we get:
d ≈ 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 (x1, y1) and (x2, y2) on a coordinate plane, you can use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, the given points are (2, 3) and (-4, -9), so we can substitute these values into the formula:
Distance = √[(-4 - 2)^2 + (-9 - 3)^2]
Simplifying further:
Distance = √[(-6)^2 + (-12)^2]
= √[36 + 144]
= √180
To round the answer to the nearest hundredth, we can use a calculator:
Distance ≈ 13.42
Therefore, the distance between (2, 3) and (-4, -9) is approximately 13.42 units.