How do you find the distance between (8,-5), (-1,-3)?

Question

Jace Anderson · Accepted Answer

undefined To find the distance between two points, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the given points (8, -5) and (-1, -3), we can substitute the values into the formula:

d = √((-1 - 8)^2 + (-3 - (-5))^2)

Simplifying further:

d = √((-9)^2 + (2)^2)

d = √(81 + 4)

d = √85

Therefore, the distance between the points (8, -5) and (-1, -3) is √85.

Isaiah Anthony · Answer

See a solution process below:

The formula for calculating the distance between two points is: #d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)# Substituting the values from the points in the problem gives: #d = sqrt((color(red)(-1) - color(blue)(8))^2 + (color(red)(-3) - color(blue)(-5))^2)# #d = sqrt((color(red)(-1) - color(blue)(8))^2 + (color(red)(-3) + color(blue)(5))^2)# #d = sqrt((-9)^2 + (2)^2)# #d = sqrt(81 + 4)# #d = sqrt(85)# Or #d = 9.220# rounded to the nearest thousandth

Ethan Adkins · Answer

undefined To find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane, you use the distance formula, which is derived from the Pythagorean theorem:

$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Given the points $(8, -5)$ and $(-1, -3)$, plug the coordinates into the formula:

$$
d = \sqrt{((-1) - 8)^2 + ((-3) - (-5))^2} \
d = \sqrt{(-9)^2 + (2)^2} \
d = \sqrt{81 + 4} \
d = \sqrt{85}
$$

Therefore, the distance between the points $(8, -5)$ and $(-1, -3)$ is $\sqrt{85}$ units.