Question

write the coordinates of the vertices after a reflection over the line x = -1.
a (□, □)
b (□, □)
c (□, □)
submit

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points \( A \), \( B \), and \( C \) from the graph.

• Point \( A \): Looking at the grid, \( A \) is at \( (-9, -7) \) (since it's 9 units left of the origin on the x - axis and 7 units down on the y - axis).
• Point \( B \): \( B \) is at \( (-1, -7) \) (1 unit left of the origin on the x - axis and 7 units down on the y - axis).
• Point \( C \): \( C \) is at \( (-9, -6) \) (9 units left of the origin on the x - axis and 6 units down on the y - axis).

Step2: Use reflection formula over \( x = a \)

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

For point \( A(-9,-7) \):

Substitute \( x=-9 \) and \( a = - 1 \) into the formula.
\( x'=2\times(-1)-(-9)=-2 + 9=7 \)
\( y'=-7 \)
So, \( A'=(7,-7) \)

For point \( B(-1,-7) \):

Substitute \( x = - 1 \) and \( a=-1 \) into the formula.
\( x'=2\times(-1)-(-1)=-2 + 1=-1 \)
\( y'=-7 \)
So, \( B'=(-1,-7) \) (since a point on the line of reflection remains the same after reflection)

For point \( C(-9,-6) \):

Substitute \( x=-9 \) and \( a = - 1 \) into the formula.
\( x'=2\times(-1)-(-9)=-2 + 9=7 \)
\( y'=-6 \)
So, \( C'=(7,-6) \)

Answer:

\( A'(7, -7) \)
\( B'(-1, -7) \)
\( C'(7, -6) \)