A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A line segment AB is shown with A as ordered pair 1, 3 and B as ordered pair 5, 3.
The line segment is reflected about the y-axis to form A′B′. Which statement describes A′B′? (4 points)
A′B′ is half the length of AB.
A′B′ and AB are equal in length.
A′B′ is greater than twice the length of AB.
A′B′ and AB are perpendicular.
The line segment AB is formed by the ordered pairs (1, 3) and (5, 3), which means it lies on the x-axis at y = 3.
To reflect a point about the y-axis, we change the sign of the x-coordinate.
So, the reflected point of A (1, 3) becomes A' (-1, 3), and the reflected point of B (5, 3) becomes B' (-5, 3).
The length of AB is 5 - 1 = 4.
The length of A'B' is |-5 - (-1)| = |-5 + 1| = 4.
Therefore, A'B' and AB are equal in length.
The correct statement is: A'B' and AB are equal in length.