Question

1. the vertices of △abc are a(-5, 4), b(-2, 4), and c(-4, 2). if △abc is reflected across the y-axis, find the coordinates of the vertex c. 6. △efg is the reflection prod 7. higher order thinking the vertices of △abc are a(-5, 5), and c(-4, 2). △abc is reflected across the y-axis and then refle again across the x-axis to produce the image △abc. what a coordinates of △abc?

Explanation:

Problem 5 (from the first visible problem about reflecting \( \triangle ABC \) over the \( y \)-axis to find \( C' \))

Step1: Recall reflection over \( y \)-axis rule

The rule for reflecting a point \( (x, y) \) across the \( y \)-axis is \( (x, y) \to (-x, y) \).

Step2: Apply the rule to point \( C \)

The coordinates of point \( C \) are \( (-4, 2) \). Using the reflection rule, we change the sign of the \( x \)-coordinate. So, \( x = -4 \) becomes \( -(-4)=4 \), and the \( y \)-coordinate remains \( 2 \).

Step1: Reflect over \( y \)-axis (rule: \( (x, y) \to (-x, y) \))

• For \( A(-5, 5) \): \( (-(-5), 5)=(5, 5) \)
• For \( B(-2, 5) \) (assumed, as per first problem's \( B(-2, 4) \) pattern, adjusted for \( y=5 \)): \( (-(-2), 5)=(2, 5) \)
• For \( C(-4, 2) \): \( (-(-4), 2)=(4, 2) \)

Step2: Reflect the new points over \( x \)-axis (rule: \( (x, y) \to (x, -y) \))

• For \( A(5, 5) \): \( (5, -5) \)
• For \( B(2, 5) \): \( (2, -5) \)
• For \( C(4, 2) \): \( (4, -2) \)

Answer:

The coordinates of vertex \( C' \) are \( (4, 2) \).

Problem 7 (reflection over \( y \)-axis then \( x \)-axis, let's assume the second vertex \( B \) is \( (-2, 5) \) as per the first problem's pattern, and solve for \( A' \), \( B' \), \( C' \))