Question

A line segment with endpoints at P (1,8) and Q (5,-2) is reflected across the y-axis and translated up 6 units. What are the coordinates of the image of point Q?

A. (-5,4)

B. (-1,14)

C. (5,8)

D (1,-2)

Answer 1

To find the image of point Q (5, -2) after reflecting it across the y-axis and then translating it up 6 units, we can follow these steps:

1. **Reflecting across the y-axis**: When a point \( (x, y) \) is reflected across the y-axis, the new coordinates become \( (-x, y) \). So, for point Q (5, -2):
\[
Q' = (-5, -2)
\]

2. **Translating up 6 units**: To translate a point \( (x, y) \) up by 6 units, you add 6 to the y-coordinate. Thus, we take the reflected point Q' = (-5, -2) and translate it:
\[
Q'' = (-5, -2 + 6) = (-5, 4)
\]

Therefore, the coordinates of the image of point Q after the transformations are \((-5, 4)\).

The correct answer is **A. (-5, 4)**.