Question

What is the distance between points (-2,3) and (-5,-1)?

Answer 1

To find the distance between the points \((-2, 3)\) and \((-5, -1)\), we can use the distance formula:

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

Here \((x_1, y_1) = (-2, 3)\) and \((x_2, y_2) = (-5, -1)\). Plugging in these values:

\[
d = \sqrt{((-5) - (-2))^2 + ((-1) - 3)^2}
\]

Calculating the differences:

\[
x_2 - x_1 = -5 + 2 = -3
\]
\[
y_2 - y_1 = -1 - 3 = -4
\]

Now substituting these back into the formula:

\[
d = \sqrt{(-3)^2 + (-4)^2}
\]
\[
d = \sqrt{9 + 16}
\]
\[
d = \sqrt{25}
\]
\[
d = 5
\]

Therefore, the distance between the points \((-2, 3)\) and \((-5, -1)\) is \(5\) units.