Question

reflection 2
triangle abc is reflected across the x - axis.
enter the new coordinates in the table and press submit to check your work.
point \t(x,y)
a \t
b \t
c \t
submit

Explanation:

Step1: Find original coordinates

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

• For point \( A \): Looking at the grid, the \( x \)-coordinate is \(-2\) and the \( y \)-coordinate is \( 1 \), so \( A = (-2, 1) \).
• For point \( B \): The \( x \)-coordinate is \(-6\) and the \( y \)-coordinate is \(-3\), so \( B = (-6, -3) \).
• For point \( C \): The \( x \)-coordinate is \( 2 \) and the \( y \)-coordinate is \(-4\), so \( C = (2, -4) \).

Step2: Apply reflection over x - axis rule

The rule for reflecting a point \((x, y)\) across the \( x \)-axis is \((x, -y)\) (the \( x \)-coordinate remains the same, and the \( y \)-coordinate is multiplied by \(-1\)).

• For \( A' \): Using the rule on \( A(-2, 1) \), we get \( A' = (-2, -1\times1)=(-2, -1) \).
• For \( B' \): Using the rule on \( B(-6, -3) \), we get \( B' = (-6, -1\times(-3)) = (-6, 3) \).
• For \( C' \): Using the rule on \( C(2, -4) \), we get \( C' = (2, -1\times(-4))=(2, 4) \).

Answer:

• \( A' \): \((-2, -1)\)
• \( B' \): \((-6, 3)\)
• \( C' \): \((2, 4)\)