Question

What is the reflection of the point (−2, 3) across the y-axis?

Enter the answers in the boxes to correctly complete the statements.

The distance from the point (−2, 3) to the x-axis is
units. The distance from the point (−2, 3) to the y-axis is units.
Question 2
To reflect across the y-axis find the point that is units from the x-axis and units from the y-axis but on the opposite side of the y-axis.
Question 3
This point is $$
.

Answer 1

• distance to x-axis: 3 units
• distance to y-axis: 2 units
• the reflected point is (2, 3)

Explanation:

The given point is (-2, 3), labeled point A in the attachment.

As you know, the distance from the x-axis is given by the y-coordinate. Here, that distance is ...

3 units from the x-axis

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The distance from the y-axis is given by the magnitude of the x-coordinate. Here, that distance is ...

2 units from the y-axis

Note that the negative coordinate value means the point is located that distance to the left of the y-axis.

__

Reflecting the point across the y-axis means choosing a point that is the same distance (2 units) right of the axis instead of left of the axis. The sign of the x-coordinate value will be positive, instead of negative. (The y-coordinate remains unchanged,)

__

The reflected point is (2, 3).

_____

Additional comment

As we have seen, reflection across the y-axis changes the sign of the x-coordinate:

(x, y) ⇒ (-x, y) . . . . reflection across the y-axis

Similarly, reflection across the x-axis changes the sigh of the y-coordinate:

(x, y) ⇒ (x, -y) . . . . reflection across the x-axis