Question

1. transform the figure using the sequence of transformation: (x,y) → (y + 1,1 − x)

Explanation:

Step1: Identify Coordinates

First, find the coordinates of points A, B, and C from the graph.

• Point A: Let's assume the grid has x and y axes. From the graph, A is at \((-3, 1)\) (since it's 3 units left of origin on x, 1 unit up on y).
• Point B: At \((-3, -1)\) (3 units left, 1 unit down).
• Point C: At \((-1, -1)\) (1 unit left, 1 unit down).

Step2: Apply Transformation

The transformation is \((x, y) \to (y + 1, 1 - x)\). Let's apply this to each point.

For Point A \((-3, 1)\):

• New x-coordinate: \(y + 1 = 1 + 1 = 2\)
• New y-coordinate: \(1 - x = 1 - (-3) = 4\)
• So, A' is \((2, 4)\)

For Point B \((-3, -1)\):

• New x-coordinate: \(y + 1 = -1 + 1 = 0\)
• New y-coordinate: \(1 - x = 1 - (-3) = 4\)
• So, B' is \((0, 4)\)

For Point C \((-1, -1)\):

• New x-coordinate: \(y + 1 = -1 + 1 = 0\)
• New y-coordinate: \(1 - x = 1 - (-1) = 2\)
• So, C' is \((0, 2)\)

Step3: Plot Transformed Points

Now, plot points A' \((2, 4)\), B' \((0, 4)\), and C' \((0, 2)\) on the grid. Connect them to get the transformed figure.

Answer:

The transformed figure has vertices at \(A'(2, 4)\), \(B'(0, 4)\), and \(C'(0, 2)\) (plot these points and connect them to see the transformed triangle).