How do you find the distance between (-1,-4), (-6,0)?

Question

Hazel Anglin · Accepted Answer

undefined To find the distance between two points, (-1,-4) and (-6,0), you can use the distance formula. The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates, we have:

d = √((-6 - (-1))^2 + (0 - (-4))^2)

Simplifying further:

d = √((-6 + 1)^2 + (0 + 4)^2)

d = √((-5)^2 + (4)^2)

d = √(25 + 16)

d = √41

Therefore, the distance between (-1,-4) and (-6,0) is √41.

Ethan Adkins · Answer

See the entire 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)(-6) - color(blue)(-1))^2 + (color(red)(0) - color(blue)(-4))^2)# #d = sqrt((color(red)(-6) + color(blue)(1))^2 + (color(red)(0) + color(blue)(4))^2)# #d = sqrt((-5)^2 + 4^2)# #d = sqrt(25 + 16)# #d = sqrt(41) = 6.403# rounded to the nearest thousandth.

Hazel Anglin · Answer

undefined To find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a Cartesian coordinate system, you can use the distance formula:

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

Given the points $(-1, -4)$ and $(-6, 0)$, you can plug the coordinates into the formula:

$$ \text{Distance} = \sqrt{(-6 - (-1))^2 + (0 - (-4))^2} $$

$$ = \sqrt{(-6 + 1)^2 + (0 + 4)^2} $$

$$ = \sqrt{(-5)^2 + 4^2} $$

$$ = \sqrt{25 + 16} $$

$$ = \sqrt{41} $$

Therefore, the distance between the points $(-1, -4)$ and $(-6, 0)$ is $\sqrt{41}$ units.