Question

two points, H and W are shown in the graph. Point W is (3,3) and point H is (-5,-3)
what is the distance between points H and W

Answer 1

To find the distance between two points \( H(-5, -3) \) and \( W(3, 3) \) in the Cartesian plane, you can use the distance formula:

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

where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of points H and W respectively.

Here, \( H(-5, -3) \) can be considered as \( (x_1, y_1) \) and \( W(3, 3) \) as \( (x_2, y_2) \).

Substituting the coordinates into the formula:

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

Calculating the differences:

\[
d = \sqrt{(3 + 5)^2 + (3 + 3)^2}
\]
\[
d = \sqrt{(8)^2 + (6)^2}
\]
\[
d = \sqrt{64 + 36}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]

Thus, the distance between points H and W is \( 10 \) units.