Question

/4 c1q4) i can describe the changes to the x- and y- coordinates of a figure after either dilation, translation, rotation or reflection. (8.g.a.3) reflections 4a. graph the reflection of abcd across the x-axis. *label your image points a, b, c, d. 4b. write the coordinates of the image abcd after the reflection. a: ____ b: __ c: __ d: ____

Explanation:

To solve this, we first identify the original coordinates of points \( A, B, C, D \) from the graph:

• \( A \): Let's assume from the grid, \( A \) is at \( (1, 4) \) (since it's 1 unit right on x - axis and 4 units up on y - axis).
• \( B \): \( (0, 5) \) (0 on x - axis, 5 on y - axis).
• \( C \): \( (-2, 1) \) (-2 on x - axis, 1 on y - axis).
• \( D \): \( (0, 0) \) (origin).

Step 1: Recall the rule for reflection over the x - axis

The rule for reflecting a point \( (x, y) \) over the x - axis is \( (x, -y) \). This means we keep the x - coordinate the same and multiply the y - coordinate by - 1.

Step 2: Find the coordinates of \( A' \)

For point \( A(1, 4) \), applying the reflection rule:
\( x = 1 \), \( y = 4 \), so \( A'=(1, - 4) \).

Step 3: Find the coordinates of \( B' \)

For point \( B(0, 5) \), applying the reflection rule:
\( x = 0 \), \( y = 5 \), so \( B'=(0, - 5) \).

Step 4: Find the coordinates of \( C' \)

For point \( C(-2, 1) \), applying the reflection rule:
\( x=-2 \), \( y = 1 \), so \( C'=(-2, - 1) \).

Step 5: Find the coordinates of \( D' \)

For point \( D(0, 0) \), applying the reflection rule:
\( x = 0 \), \( y = 0 \), so \( D'=(0, 0) \) (since \( - 0=0 \)).

Answer:

\( A' \): \( (1, - 4) \)
\( B' \): \( (0, - 5) \)
\( C' \): \( (-2, - 1) \)
\( D' \): \( (0, 0) \)