Question

the figure below is dilated by a factor of \\(\frac{1}{4}\\) centered at the origin. plot the resulting image. click twice to plot a segment. click a segment to delete it. answer attempt 1 out of 3

Explanation:

Step1: Identify Coordinates of Original Points

First, we need to find the coordinates of points \( Q \), \( P \), \( O \), and \( N \) from the graph.

• Point \( Q \): From the graph, it looks like \( Q(-3, 8) \) (assuming the grid lines, moving 3 units left on x - axis and 8 units up on y - axis).
• Point \( P \): \( P(4, 4) \) (4 units right on x - axis and 4 units up on y - axis).
• Point \( O \): \( O(8, - 8) \) (8 units right on x - axis and 8 units down on y - axis).
• Point \( N \): \( N(-3, - 8) \) (3 units left on x - axis and 8 units down on y - axis).

Step2: Apply Dilation Formula

The rule for dilation centered at the origin with a scale factor \( k=\frac{1}{4}\) is \((x,y)\to(kx,ky)\).

• For point \( Q(-3,8)\):

New \( x \) - coordinate: \( \frac{1}{4}\times(-3)=-\frac{3}{4} \)
New \( y \) - coordinate: \( \frac{1}{4}\times8 = 2 \)
So, \( Q'(-\frac{3}{4},2) \)

• For point \( P(4,4)\):

New \( x \) - coordinate: \( \frac{1}{4}\times4 = 1 \)
New \( y \) - coordinate: \( \frac{1}{4}\times4=1 \)
So, \( P'(1,1) \)

• For point \( O(8, - 8)\):

New \( x \) - coordinate: \( \frac{1}{4}\times8 = 2 \)
New \( y \) - coordinate: \( \frac{1}{4}\times(-8)=-2 \)
So, \( O'(2,-2) \)

• For point \( N(-3, - 8)\):

New \( x \) - coordinate: \( \frac{1}{4}\times(-3)=-\frac{3}{4} \)
New \( y \) - coordinate: \( \frac{1}{4}\times(-8)=-2 \)
So, \( N'(-\frac{3}{4},-2) \)

Step3: Plot the New Points

Plot the points \( Q'(-\frac{3}{4},2) \), \( P'(1,1) \), \( O'(2,-2) \), and \( N'(-\frac{3}{4},-2) \) on the coordinate plane and connect them in the same order as the original figure to get the dilated image.

Answer:

To plot the dilated figure, plot the points \( Q'(-\frac{3}{4},2) \), \( P'(1,1) \), \( O'(2,-2) \), and \( N'(-\frac{3}{4},-2) \) and connect them. (Note: Since this is a plotting task, the final answer is the set of plotted points as calculated above.)