Question

question 2 (3 points) find the coordinates of triangle abc after a reflection over the y-axis.

Explanation:

Step1: Identify original coordinates

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

• Point \( A \): Looking at the grid, the \( x \)-coordinate is \(-3\) and the \( y \)-coordinate is \(-1\), so \( A(-3, -1) \).
• Point \( B \): The \( x \)-coordinate is \( 0 \) and the \( y \)-coordinate is \(-3\), so \( B(0, -3) \).
• Point \( C \): The \( x \)-coordinate is \(-2\) and the \( y \)-coordinate is \(-4\), so \( C(-2, -4) \).

Step2: Apply reflection over y - axis rule

The rule for reflecting a point \((x, y)\) over the \( y \)-axis is \((x, y)\to(-x, y)\). This means we change the sign of the \( x \)-coordinate while keeping the \( y \)-coordinate the same.

• For point \( A(-3, -1) \): Applying the rule, we get \( A'(-(-3), -1)=(3, -1) \).
• For point \( B(0, -3) \): Applying the rule, we get \( B'(-0, -3)=(0, -3) \) (since \(-0 = 0\)).
• For point \( C(-2, -4) \): Applying the rule, we get \( C'(-(-2), -4)=(2, -4) \).

Answer:

The coordinates of triangle \( ABC \) after reflection over the \( y \)-axis are \( A'(3, -1) \), \( B'(0, -3) \), and \( C'(2, -4) \).