Question

Use the image to answer the 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.
Remaining Attempts : 3
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page 17 of 18

Answer 1

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

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

Here, \( A(1, 5) \) gives us \( (x_1, y_1) = (1, 5) \) and \( B(5, 2) \) gives us \( (x_2, y_2) = (5, 2) \).

Now, substituting the coordinates:

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

Calculating the differences:

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

Calculating the squares:

\[
d = \sqrt{16 + 9}
\]

Adding the values:

\[
d = \sqrt{25}
\]

Taking the square root:

\[
d = 5
\]

Thus, the distance between points \( A \) and \( B \) is \( 5 \) units.