Question

Line segment AB is shown on a coordinate grid:

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.

Answer 1

A′B′ and AB are equal in length.

Explanation:

Answer 2

The statements which describe A'B' is:

A'B' and AB are equal in length ⇒ (B)

Explanation:

Let us take about reflication:

⇒ Reflections are mirror images, means the shape or the size of

the figure does not affect by reflection, think of "folding" the

graph over the y-axis or the x-axis

⇒ On a grid, you used the formula (x, y) → (-x, y) for a reflection in

the y-axis and used the formula (x, y) → (x, -y) for a reflection in

the x-axis.

In our question segment AB, where A = (1, 3) and B = (5, 3) is

reflected about the y-axis

By using the rule above

∴ A' =(-1, 3)

∴ B' = (-5,3)

∵ Reflection does not change the shape or the size of the original figure

∴ Line segment A'B' has the same length of line segment AB

The correct answer is:

A'B' and AB are equal in length

You can check your answer by finding the lengths of AB and A'B'

∵ The length of AB = 5 - 1 = 4 units

∵ The length of A'B' = -1 - (-5) = -1 + 5 = 4 units

∴ AB = A'B'

Note:

If the y-coordinates of two points are equal, then the line joining them is horizontal and its length is the difference between the x-coordinates of the two points.