Question

8-2 practice exercises (lms graded)
8-2 reflections
what is the image of a(2, 1) after reflecting it across x = 4 and then across the x-axis?
a. (-6, 1)
b. (6, 1)
c. (6, -1)
d. (-6, -1)

Explanation:

Step1: Reflect across \( x = 4 \)

The formula for reflecting a point \( (x,y) \) across the vertical line \( x = a \) is \( (2a - x,y) \). Here, \( a = 4 \) and the point is \( A(2,1) \). So, \( x' = 2\times4 - 2 = 8 - 2 = 6 \), \( y' = 1 \). The new point after first reflection is \( (6,1) \).

Step2: Reflect across the \( x \)-axis

The formula for reflecting a point \( (x,y) \) across the \( x \)-axis is \( (x,-y) \). Using the point \( (6,1) \), we get \( x'' = 6 \), \( y'' = -1 \). So the final point is \( (6,-1) \).

Answer:

C. \( (6, -1) \)