Question

Given the point S, state the coordinates of S" after it has been reflected across the y-axis, then translated by (x + 5, y + 2)

C

Answer 1

(-x + 5, y + 2)

Explanation:

To find the coordinates of S" after reflecting across the y-axis and then translating by (x + 5, y + 2), you can follow these steps:

Reflect across the y-axis: When you reflect a point across the y-axis, you change the sign of the x-coordinate while keeping the y-coordinate the same.

So, if the original point S is (x, y), after reflecting across the y-axis, it becomes (-x, y).

Translate by (x + 5, y + 2): This means you add 5 to the x-coordinate and 2 to the y-coordinate.

So, if the reflected point is (-x, y), after the translation, it becomes (-x + 5, y + 2).

Therefore, the coordinates of S" after reflecting across the y-axis and then translating by (x + 5, y + 2) are (-x + 5, y + 2).

Answer 2

To reflect a point across the y-axis, we change the sign of the x-coordinate and keep the y-coordinate the same.

Let's denote the point S as (x, y).

Reflecting S across the y-axis: The x-coordinate of S" will be the negative of the x-coordinate of S, and the y-coordinate will remain the same. So, the coordinates of S" after reflecting across the y-axis will be (-x, y).

Translating S" by (x + 5, y + 2): To translate a point, we add the given translations to the coordinates of the point.

The new x-coordinate of S" will be (-x + 5), and the new y-coordinate will be (y + 2).

Therefore, the coordinates of S" after reflecting across the y-axis and translating by (x + 5, y + 2) are: (-x + 5, y + 2).