Question

where will point c be after a reflection over the line $y = -1$?

Explanation:

Step1: Find coordinates of point C

From the graph, point \( C \) has coordinates \( (6, 1) \) (since it's at \( x = 6 \), \( y = 1 \)).

Step2: Recall reflection over horizontal line \( y = k \)

The formula for reflecting a point \( (x, y) \) over the line \( y = k \) is \( (x, 2k - y) \). Here, \( k = -1 \), \( x = 6 \), \( y = 1 \).

Step3: Calculate new y - coordinate

Substitute into the formula: \( 2(-1)-1=-2 - 1=-3 \). The x - coordinate remains the same (\( x = 6 \)).

Answer:

The coordinates of the reflected point \( C \) are \( (6, - 3) \)