Question

dilate △fgh by a scale factor of 4 with the center of dilation at the origin. graph the dilation.

Explanation:

Step1: Find coordinates of original points

First, identify the coordinates of \( F \), \( G \), and \( H \) from the graph.

• \( F \): From the grid, \( x = -2 \), \( y = -1 \), so \( F(-2, -1) \)
• \( G \): \( x = -1 \), \( y = 0 \), so \( G(-1, 0) \)
• \( H \): \( x = -1 \), \( y = -2 \), so \( H(-1, -2) \)

Step2: Apply dilation with scale factor 4 (center at origin)

The rule for dilation with scale factor \( k \) centered at the origin is \( (x, y) \to (k \cdot x, k \cdot y) \). Here, \( k = 4 \).

• For \( F(-2, -1) \): New coordinates \( F' = (4 \cdot (-2), 4 \cdot (-1)) = (-8, -4) \)
• For \( G(-1, 0) \): New coordinates \( G' = (4 \cdot (-1), 4 \cdot 0) = (-4, 0) \)
• For \( H(-1, -2) \): New coordinates \( H' = (4 \cdot (-1), 4 \cdot (-2)) = (-4, -8) \)

Step3: Graph the new points

Plot \( F'(-8, -4) \), \( G'(-4, 0) \), and \( H'(-4, -8) \) on the coordinate plane and connect them to form the dilated triangle \( \triangle F'G'H' \).

Answer:

To dilate \( \triangle FGH \) with a scale factor of 4 centered at the origin:

1. Find original coordinates: \( F(-2, -1) \), \( G(-1, 0) \), \( H(-1, -2) \).
2. Apply dilation rule \( (x, y) \to (4x, 4y) \):

• \( F'(-8, -4) \), \( G'(-4, 0) \), \( H'(-4, -8) \).

1. Graph these new points and connect them to form the dilated triangle.

(Note: The graphing step involves plotting \( (-8, -4) \), \( (-4, 0) \), and \( (-4, -8) \) and drawing the triangle.)