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, we can use the distance formula, which is given by:
\(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Plugging in the coordinates of the points \((-8,-3)\) and \((-2,-5)\), we have:
\(\sqrt{(-2-(-8))^2+(-5-(-3))^2}\)
Simplifying inside the square root, we have:
\(\sqrt{(6)^2+(-2)^2}\)
Calculating the squares, we have:
\(\sqrt{36+4}\)
Simplifying inside the square root, we have:
\(\sqrt{40}\)
Since \(\sqrt{40}\) is not a perfect square, we cannot simplify it further.
To round the answer to the nearest hundredth, we evaluate \(\sqrt{40}\) using a calculator:
\(\sqrt{40} \approx 6.32\)
Therefore, the distance between \((-8,-3)\) and \((-2,-5)\) is approximately 6.32 (rounded to the nearest hundredth).
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 and can be stated as follows:
Distance = √((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). Let's label them as follows:
Point 1: (x1, y1) = (-8, -3)
Point 2: (x2, y2) = (-2, -5)
Now, substitute the values into the distance formula:
Distance = √((-2 - (-8))^2 + (-5 - (-3))^2)
Simplifying further:
Distance = √((6)^2 + (-5 + 3)^2)
Distance = √(36 + 4)
Distance = √(40)
Now, calculate the square root of 40:
Distance ≈ 6.32 (rounded to the nearest hundredth)
Therefore, the distance between the points (-8, -3) and (-2, -5) is approximately 6.32 units.
To find the distance between two points, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance using this formula:
Distance = sqrt((-2 - (-8))^2 + (-5 - (-3))^2)
Simplifying inside the square root:
Distance = sqrt((6)^2 + (-2)^2)
Calculating the squares:
Distance = sqrt(36 + 4)
Distance = sqrt(40)
Using a calculator, we find:
Distance ≈ 6.32
Therefore, the distance between the points (-8, -3) and (-2, -5) is approximately 6.32.