Question

the figure below is dilated by a factor of 2 centered at the origin. plot the resulting image.
click twice to plot a segment.
click a segment to delete it.

Explanation:

Step1: Identify coordinates of original points

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

• \( P(0, 2) \) (since it's on the y - axis, x = 0, y = 2)
• \( Q(-1, 2) \) (x=-1, y = 2)
• \( N(-3, -2) \) (x=-3, y=-2)
• \( O(4, -2) \) (x = 4, y=-2)

Step2: Apply dilation formula

The rule for dilation centered at the origin with a scale factor \( k \) is \( (x,y)\to(kx,ky) \). Here, \( k = 2 \).

• For point \( P(0,2) \):

New coordinates \( P'=(2\times0,2\times2)=(0,4) \)

• For point \( Q(-1,2) \):

New coordinates \( Q'=(2\times(-1),2\times2)=(-2,4) \)

• For point \( N(-3,-2) \):

New coordinates \( N'=(2\times(-3),2\times(-2))=(-6,-4) \)

• For point \( O(4,-2) \):

New coordinates \( O'=(2\times4,2\times(-2))=(8,-4) \)

Step3: Plot the new points

Now we plot the points \( P'(0,4) \), \( Q'(-2,4) \), \( N'(-6,-4) \), and \( O'(8,-4) \) and connect them as per the original figure's shape (a quadrilateral, so connect \( Q' \) to \( P' \), \( P' \) to \( O' \), \( O' \) to \( N' \), \( N' \) to \( Q' \) or as per the original connection).

Answer:

The dilated image has vertices at \( P'(0,4) \), \( Q'(-2,4) \), \( N'(-6,-4) \), and \( O'(8,-4) \). (To plot, mark these points on the coordinate plane and connect them appropriately.)