Question

On a coordinate plane, point A is 2 units to the left and 5 units up. Point B is 5 units to the right and 5 units up.
What is the distance between the points?

Point A is located at the point
.
Point B is located at the point
.
The distance between the points is
units.

Answer 1

To find the coordinates of points A and B based on the given information, let's assume that we are starting from the origin (0, 0).

**Point A** is located 2 units to the left (negative direction on the x-axis) and 5 units up (positive direction on the y-axis). Therefore, the coordinates of Point A are:
\[
A = (-2, 5)
\]

**Point B** is located 5 units to the right (positive direction on the x-axis) and 5 units up (positive direction on the y-axis). Therefore, the coordinates of Point B are:
\[
B = (5, 5)
\]

Now, to find the distance between the two points A and B, we can use the distance formula:
\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
where \( (x_1, y_1) \) are the coordinates of point A and \( (x_2, y_2) \) are the coordinates of point B.

Substituting the coordinates into the formula:
\[
\text{Distance} = \sqrt{(5 - (-2))^2 + (5 - 5)^2}
\]
\[
= \sqrt{(5 + 2)^2 + (0)^2}
\]
\[
= \sqrt{(7)^2 + 0}
\]
\[
= \sqrt{49}
\]
\[
= 7
\]

Thus, the distance between the points is 7 units.

In conclusion:
- Point A is located at the point \((-2, 5)\).
- Point B is located at the point \((5, 5)\).
- The distance between the points is \(7\) units.