Question

Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with the origin as the center of dilation using the rule (x,y) —> (1/4 x, 1/4y) to create pentagon M’N’P’Q’R

Read each statement below
if it is TRUE, circle GREEN, if it is FALSE, circle Red

Pentagon M’N’P’Q’R is larger than pentagon MNPQR, because the scale factor is greater than 1

Pentagon M’N’P’Q’R is smaller than pentagon MNPQR, because the scale factor is less than 1.

Pentagon M’N’P’G’R is smaller than pentagon MNPQR, because the scale factor is greater than 1

Pentagon M’N’P’Q’R is larger than pentagon MNPQR because the scale factor is less than 1

If someone could help me with this whole test right now that would be REALLY helpful since it’s due in a couple hours

Answer 1

Option (2)

Explanation:

If a polygon is dilated by a scale factor = k

Rule to be followed,

(x, y) → (kx, ky)

Here, k = Scale factor

If 0 < k < 1, size of the image will be reduced.

If k > 1, size of the image will be enlarged.

Pentagon MNPQR is dilated with the origin as the center of dilation to form an image M'N'P'Q'R'.

Rule used for the transformation,

(x, y) →
`((1)/(4)x,(1)/(4)y)`

Here, scale factor by which MNPQR has been dilated is
`(1)/(4)`

Since, scale factor is between 0 and
`(1)/(4)`, size of M'N'P'Q'R' will be reduced.

Therefore, size of pentagon M'N'P'Q'R' will be smaller than pentagon MNPQR.

Option (2) will be the answer.