Find the distance between (-8,-3) and (-2,-5). Round your answer to the nearest hundredth, if necessary.
To find the distance between two points (-8, -3) and (-2, -5), you can use the distance formula.
The distance formula is given by:
d = √((x2 - x1)² + (y2 - y1)²)
Let's substitute the values into the formula:
d = √((-2 - (-8))² + (-5 - (-3))²)
Simplifying:
d = √((6)² + (-2)²)
d = √(36 + 4)
d = √40
Now, let's round the answer to the nearest hundredth:
d ≈ 6.32
Therefore, the distance between (-8, -3) and (-2, -5) is approximately 6.32 units.
Using the distance formula, the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. In this case, $x_1 = -8$, $y_1 = -3$, $x_2 = -2$, and $y_2 = -5$. Plugging in these values, we get $\sqrt{(-2-(-8))^2 + (-5-(-3))^2} = \sqrt{6^2 + (-2)^2} = \sqrt{40} \approx \boxed{6.32}$.
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, which states that the square of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides.
The distance formula is given as:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the coordinates of the first point are (-8, -3), and the coordinates of the second point are (-2, -5).
Substituting these values into the distance formula, we have:
d = √((-2 - (-8))² + (-5 - (-3))²)
Simplifying further:
d = √((-2 + 8)² + (-5 + 3)²)
d = √(6² + (-2)²)
d = √(36 + 4)
d = √40
To round the answer to the nearest hundredth, we can use a calculator or express the square root of 40 as a decimal:
d ≈ 6.32 (rounded to the nearest hundredth)