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?

Question

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).