Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.
d(□, □)
e(□, □)
f(□, □)

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points \( D \), \( E \), and \( F \) from the graph.

• For point \( D \): Looking at the graph, \( D \) is at \( (-2, -1) \)? Wait, no, wait. Wait, the grid: Let's check again. Wait, \( D \) is on the x=-2, y=-1? Wait, no, the y-axis: Wait, the grid lines. Wait, \( D \) is at \( (-2, -1) \)? Wait, no, maybe I misread. Wait, the original points: Let's see, \( D \) is at \( (-2, -1) \)? Wait, no, looking at the graph, \( D \) is at \( (-2, -1) \)? Wait, no, maybe \( D \) is \( (-2, -1) \), \( E \) is \( (2, -1) \), \( F \) is \( (-2, 1) \)? Wait, let's check the graph again. The point \( D \) is at x=-2, y=-1? Wait, the vertical line for \( D \) is x=-2, horizontal line is y=-1? Wait, no, the y-axis: the grid lines. Let's see, the original coordinates:
• \( D \): x=-2, y=-1? Wait, no, maybe \( D \) is \( (-2, -1) \), \( E \) is \( (2, -1) \), \( F \) is \( (-2, 1) \). Wait, let's confirm. The dilation is centered at the origin with scale factor 4. The rule for dilation centered at the origin is \( (x, y)

ightarrow (k \cdot x, k \cdot y) \), where \( k \) is the scale factor.

Wait, maybe I made a mistake. Let's look at the graph again. The point \( D \): the x-coordinate is -2, y-coordinate is -1? Wait, no, the y-axis: the grid lines. Let's see, the original \( D \) is at \( (-2, -1) \)? Wait, no, maybe \( D \) is \( (-2, -1) \), \( E \) is \( (2, -1) \), \( F \) is \( (-2, 1) \). Let's check:

• \( D \): x=-2, y=-1
• \( E \): x=2, y=-1
• \( F \): x=-2, y=1

Now, dilation with scale factor 4 centered at origin: multiply each coordinate by 4.

Step2: Apply dilation to \( D \)

For point \( D(-2, -1) \), after dilation: \( x' = 4 \times (-2) = -8 \), \( y' = 4 \times (-1) = -4 \). So \( D'(-8, -4) \).

Step3: Apply dilation to \( E \)

For point \( E(2, -1) \), after dilation: \( x' = 4 \times 2 = 8 \), \( y' = 4 \times (-1) = -4 \). So \( E'(8, -4) \).

Step4: Apply dilation to \( F \)

For point \( F(-2, 1) \), after dilation: \( x' = 4 \times (-2) = -8 \), \( y' = 4 \times 1 = 4 \). So \( F'(-8, 4) \).

Wait, but maybe I misread the original coordinates. Let's check again. Maybe the original \( D \) is \( (-2, -1) \), \( E \) is \( (2, -1) \), \( F \) is \( (-2, 1) \). Let's confirm with the graph. The point \( D \) is at x=-2, y=-1 (since it's on the horizontal line y=-1 and vertical line x=-2). \( E \) is at x=2, y=-1. \( F \) is at x=-2, y=1 (on vertical line x=-2, horizontal line y=1). So yes, original coordinates: \( D(-2, -1) \), \( E(2, -1) \), \( F(-2, 1) \).

Now, applying dilation with scale factor 4 (multiply each coordinate by 4):

• \( D' \): \( (4 \times -2, 4 \times -1) = (-8, -4) \)
• \( E' \): \( (4 \times 2, 4 \times -1) = (8, -4) \)
• \( F' \): \( (4 \times -2, 4 \times 1) = (-8, 4) \)

Answer:

\( D'(-8, -4) \), \( E'(8, -4) \), \( F'(-8, 4) \)