Question

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

Explanation:

Step1: Identify coordinates of original points

First, we find the coordinates of \( F \), \( G \), and \( H \) from the graph. Let's assume:

• \( F(-2, -1) \) (wait, looking at the graph, maybe better to check the grid. Wait, the x-axis: from left, the points: \( F \) seems at (-2, -1)? Wait, no, the graph has x from -10 to 0, y from -10 to 0? Wait, maybe the coordinates are: Let's re-examine. The origin is at (0,0). \( F \) is at (-2, -1)? Wait, no, the blue dot for \( F \) is at x=-2, y=-1? Wait, \( G \) is at (-1, 0), \( H \) is at (-1, -2)? Wait, maybe I misread. Wait, the grid: each square is 1 unit? Let's check the coordinates:

Looking at the graph:

• \( F \): x = -2, y = -1 (since it's 2 units left of origin, 1 unit down)
• \( G \): x = -1, y = 0 (1 unit left of origin, on x-axis)
• \( H \): x = -1, y = -2 (1 unit left of origin, 2 units down)

Wait, maybe better to get the correct coordinates. Let's see: the x-axis is from -10 to 0 (left to right), y-axis from -10 to 0 (bottom to top? Wait, no, usually y-axis is up positive, but here the graph shows y from -10 at the bottom to 0 at the top? Wait, maybe the coordinates are:

Wait, the point \( F \) is at (-2, -1)? Wait, no, the blue dot for \( F \) is at x=-2, y=-1? Wait, \( G \) is at (-1, 0), \( H \) is at (-1, -2). Let's confirm:

So original coordinates:

• \( F(-2, -1) \)
• \( G(-1, 0) \)
• \( H(-1, -2) \)

Step2: Apply dilation with scale factor 4, center at origin

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

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:

The dilated triangle \( \triangle F'G'H' \) has vertices at \( F'(-8, -4) \), \( G'(-4, 0) \), and \( H'(-4, -8) \). To graph it, plot these points and connect them.