Question

determining the new points
if triangle abc is translated down 3 units and then reflected across the y - axis, what are the coordinates of point a?
(□,□)
if triangle abc is translated down 3 units and then reflected across the y - axis, what are the coordinates of point b?
(2,□)
if triangle abc is translated down 3 units and then reflected across the y - axis, what are the coordinates of point c?
(□,□)

Explanation:

Step1: Find Original Coordinates

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

• Point \( A \): \( (1, 5) \) (since it's 1 unit right on \( x \)-axis, 5 units up on \( y \)-axis).
• Point \( B \): \( (4, 2) \) (4 units right, 2 units up).
• Point \( C \): \( (1, 1) \) (1 unit right, 1 unit up).

Step2: Translate Down 3 Units

Translation down 3 units means subtracting 3 from the \( y \)-coordinate.

• For \( A \): New \( y \)-coordinate \( = 5 - 3 = 2 \), so translated \( A \): \( (1, 2) \).
• For \( B \): New \( y \)-coordinate \( = 2 - 3 = -1 \), so translated \( B \): \( (4, -1) \).
• For \( C \): New \( y \)-coordinate \( = 1 - 3 = -2 \), so translated \( C \): \( (1, -2) \).

Step3: Reflect Across \( y \)-axis

Reflection across \( y \)-axis changes \( x \)-coordinate to its opposite (multiply by \( -1 \)), \( y \)-coordinate remains.

• For \( A \): New \( x \)-coordinate \( = -1 \), so reflected \( A' \): \( (-1, 2) \).
• For \( B \): New \( x \)-coordinate \( = -4 \), so reflected \( B' \): \( (-4, -1) \).
• For \( C \): New \( x \)-coordinate \( = -1 \), so reflected \( C' \): \( (-1, -2) \).

For Point \( A' \):

Answer:

\((-1, 2)\)

For Point \( B' \):