In the standard (x, y) coordinate plane, a parallelogram ABCD has vertices A(-6, -3), B(1,… — ACT

In the standard $(x, y)$ coordinate plane, a parallelogram $ABCD$ has vertices $A(-6, -3)$ , $B(1, -3)$ , $C(6, 2)$ , and $D(-1, 2)$ . What is the length of the diagonal $AC$ ?

Answer: 13

Answer

The correct answer is 13.

The length of the diagonal

AC

is found by calculating the distance between the vertices

A(-6, -3)

and

C(6, 2)

. Using the distance formula:

AC = \sqrt{(6 - (-6))^2 + (2 - (-3))^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13

Step-by-Step Solution

Identify the coordinates of the endpoints of diagonal

AC

A(-6, -3)

and

C(6, 2)

The diagonal of a polygon connects non-adjacent vertices, so the diagonal

AC

connects vertex

A

to vertex

C

Use the distance formula to find the length of the segment

AC

AC = \sqrt{(6 - (-6))^2 + (2 - (-3))^2}

The distance formula calculates the straight-line distance between two points on the coordinate plane.

Simplify the expression to find the final integer length.

13

Calculating the squares and summing them gives

\sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13

Key Concept

Calculating the length of a geometric segment on the coordinate plane using the distance formula.

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