Question

11 practice 4 (from unit 6, lesson 2)
b. $(x, y) \to (y, x)$
type your answers in the boxes.
$a$ : ( , )
$b$ : ( , )
$c$ : ( , )
c. $(x, y) \to (1.5x, 1.5y)$
type your answers in the boxes.
$a$ : ( , )
$b$ : ( , )
$c$ : ( , )
triangle $abc$ is shown on the graph. graph each of the images on the same graph.
to graph a triangle, use the polygon tool by graphing each of the vertices of the triangle, making sure to connect the last vertex to the first vertex.

Explanation:

To solve this, we need the coordinates of triangle \( ABC \). Since the graph isn't fully visible, let's assume typical coordinates (e.g., \( A(x_1,y_1) \), \( B(x_2,y_2) \), \( C(x_3,y_3) \)) and apply the transformations.

Part b: \((x,y) \to (y,x)\) (Reflection over \( y = x \))

Step 1: Identify \( A, B, C \) coordinates

Assume \( A(2,1) \), \( B(4,3) \), \( C(1,4) \) (common triangle coordinates; adjust if needed).

Step 2: Apply transformation to \( A \)

\( A'(y_A, x_A) = (1, 2) \)

Step 3: Apply transformation to \( B \)

\( B'(y_B, x_B) = (3, 4) \)

Step 4: Apply transformation to \( C \)

\( C'(y_C, x_C) = (4, 1) \)

Part c: \((x,y) \to (1.5x, 1.5y)\) (Dilation by factor 1.5)

Step 1: Use same \( A, B, C \)

\( A(2,1) \), \( B(4,3) \), \( C(1,4) \)

Step 2: Dilate \( A \)

\( A'(1.5 \times 2, 1.5 \times 1) = (3, 1.5) \)

Step 3: Dilate \( B \)

\( B'(1.5 \times 4, 1.5 \times 3) = (6, 4.5) \)

Step 4: Dilate \( C \)

\( C'(1.5 \times 1, 1.5 \times 4) = (1.5, 6) \)

Answer:

(assuming \( A(2,1) \), \( B(4,3) \), \( C(1,4) \)):

Part b:

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

Part c:

\( A' : (3, 1.5) \)
\( B' : (6, 4.5) \)
\( C' : (1.5, 6) \)

(Note: Replace coordinates with actual graph’s \( A, B, C \) for precision.)