Question

What does the algebraic representation (x,y) → (-x, y) represent?

Answer 1

Answer:

The given algebraic representation (x,y) → (-x, y) represents the reflection of a point (x, y) across the y-axis.

Step-by-step explanation:

We know that when a point P(x, y) is reflected across the y-axis, the x-coordinate changes/reverses its sign, but the y-coordinate stays the same.

Thus, the rule of reflection of a point P(x, y) across y-xis is:

P(x, y) → P'(-x, y)

For example, if a point A(1, 2) is reflected across the y-axis, the coordinates of the image A' of the point A(1, 2) will be:

A(1, 2)  → A'(-1, y)

In our case, we are given the  algebraic representation

(x,y) → (-x, y)

Here:

• The x-coordinate changes/reverses its sign

• The y-coordinate stays the same.

Thus, the given algebraic representation (x,y) → (-x, y) represents the reflection of a point (x, y) across the y-axis.