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Pentagon MVEDR is shown on the coordinate grid. Pentagon MVEDR is dilated with the origin as the center of dilation using the rule (x,y)→(23x, 23y) to create pentagon M'V'E'D'R'.

Which statement is true?


Pentagon M'V'E'D'R' is larger than pentagon MVEDR because the scale factor is greater than 1.

Pentagon M'V'E'D'R' is smaller than pentagon MVEDR because the scale factor is less than 1.

Pentagon M'V'E'D'R' is larger than pentagon MVEDR because the scale factor is less than 1.

Pentagon M'V'E'D'R' is smaller than pentagon MVEDR because the scale factor is greater than 1.
Coordinate plane with 4 quadrants. x-axis runs from negative 6 to 4 and y-axis runs from negative 5 to 5 and arrows on both ends. Pentagon with vertices at M at negative 5 comma 2, v at negative 2 comma 3, e at 3 comma 3, d at 3 comma negative 3, r at negative 2 comma negative 3 Vertices labeled with letters.

Given:

Consider the pentagon MVEDR is dilated with the origin as the center of dilation using the rule [tex](x,y)\to(\dfrac{2}{3}x,\dfrac{2}{3}y)[/tex] to create pentagon M'V'E'D'R'.

To find:

The correct statement.

Solution:

If a figure dilated by factor k, then the rule of dilation is

[tex](x,y)\to (kx,ky)[/tex]

Here,

If k>1, then the image is larger than the original figure.

If k<1, then the image is smaller than the original figure.

We have,

[tex](x,y)\to(\dfrac{2}{3}x,\dfrac{2}{3}y)[/tex]

Here, M'V'E'D'R' is image and MVEDR is original figure. The scale factor is

[tex]k=\dfrac{2}{3}<1[/tex]

Pentagon M'V'E'D'R' is smaller than pentagon MVEDR because the scale factor is less than 1.

Therefore, the correct option is B.

  Option (B). Pentagon M'V'E'D'R' is smaller than pentagon MVDER because the scale factor is less than 1.

           image point formed will follow the rule,

           (x, y) → (kx, ky)

            If k < 1, image will be smaller than the preimage.

Given in the question,

Rule for the transformation → [tex](x,y)\rightarrow (\frac{2}{3}x,\frac{2}{3}y)[/tex]

Here, [tex]k=\frac{2}{3}[/tex] which is less than 1.

      Therefore, image pentagon M'V'E'D'R' will be smaller than the original pentagon MVDER.

      Option (B) will be the correct option.

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