Use the image to answer the question.

Question

A straight, solid line connects plotted points upper A and upper B on a coordinate plane. The line slopes downward from left to right in quadrant 1. Point upper A is left parenthesis 1 comma 5 right parenthesis. Point upper B is left parenthesis 5 comma 2 right parenthesis.

What is the distance between the two points shown on the grid?

(1 point)
The distance between the points is
units.

Answer 1

To find the distance between the two points \( A(1, 5) \) and \( B(5, 2) \), we can use the distance formula:

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

where \( (x_1, y_1) = (1, 5) \) and \( (x_2, y_2) = (5, 2) \).

Substituting the values into the formula:

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

Calculating the differences:

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

Therefore, the distance between the two points is \( \boxed{5} \) units.