Question

graphing an enlargement with given scale factor
scale factor = 2
pre - image
consider the given pre - image dilated by a scale factor of 2, and answer the questions.
after applying the scale factor, what is the image?
what will be the new coordinate of the vertex at (3, 3) if the vertex at (0, 0) remains the same?

Explanation:

For the first question (After applying the scale factor, what is the image?):

Dilation with a scale factor of 2 means each side length of the pre - image (a square, likely) will be multiplied by 2. So the image is an enlargement (a larger square) of the pre - image with all linear dimensions doubled.

Step1: Recall the dilation rule

When a figure is dilated with a scale factor \(k\) and the center of dilation is the origin \((0,0)\), the rule for a point \((x,y)\) is \((x,y)\to(kx,ky)\). Here, \(k = 2\) and the point is \((3,3)\).

Step2: Apply the dilation rule

For the \(x\) - coordinate: \(x_{new}=2\times3 = 6\)
For the \(y\) - coordinate: \(y_{new}=2\times3 = 6\)

Answer:

An enlarged square (or a dilated image of the pre - image square with scale factor 2)

For the second question (What will be the new coordinate of the vertex at (3, 3) if the vertex at (0, 0) remains the same?):