Question

deltamath back to home rigid transformations extra credit due september 12 at 8:00 pm grade: 75% reflect figure over a line (level 1) points reflected over an axis (graphically) click on the graph to plot a point. click a point to delete it.

Explanation:

To solve the problem of reflecting point \( E \) over the \( x \)-axis, we follow these steps:

Step 1: Identify the coordinates of point \( E \)

From the graph, point \( E \) is at \( (-6, -4) \) (since it is 6 units left on the \( x \)-axis and 4 units down on the \( y \)-axis).

Step 2: Apply the reflection rule over the \( x \)-axis

The rule for reflecting a point \( (x, y) \) over the \( x \)-axis is:
\[ (x, y)
ightarrow (x, -y) \]
This means we keep the \( x \)-coordinate the same and reverse the sign of the \( y \)-coordinate.

Step 3: Calculate the reflected coordinates

For point \( E(-6, -4) \):

• The \( x \)-coordinate remains \( -6 \).
• The \( y \)-coordinate becomes \( -(-4) = 4 \).

Thus, the reflected point is \( (-6, 4) \).

Step 4: Plot the reflected point

On the graph, locate \( x = -6 \) and \( y = 4 \), then plot the point.

Answer:

The reflected point over the \( x \)-axis is \( \boldsymbol{(-6, 4)} \). To plot it, click on the coordinate \( (-6, 4) \) on the graph.