Question

1 the vertices of a figure are given. what are the coordinates of the image after the given dilation? identify the type of dilation. m(2,3), n(5,3), p(5,1) k=3 type of dilation: dropdown diagram with rectangles labeled m, n, p and a smaller rectangle, and type of dilation: with a dropdown arrow

Explanation:

Step1: Recall dilation rule

For a dilation with scale factor \( k \), the coordinates \((x,y)\) of a point transform to \((k \cdot x, k \cdot y)\) (assuming the center of dilation is the origin; since no other center is given, we assume origin).

Step2: Dilate point M(2,3)

Multiply each coordinate by \( k = 3 \): \( M'=(3\times2, 3\times3)=(6,9) \)

Step3: Dilate point N(5,3)

Multiply each coordinate by \( 3 \): \( N'=(3\times5, 3\times3)=(15,9) \)

Step4: Dilate point P(5,1)

Multiply each coordinate by \( 3 \): \( P'=(3\times5, 3\times1)=(15,3) \)

Step5: Identify dilation type

Since \( k = 3>1 \), the dilation is an enlargement (or expansion).

Answer:

Coordinates of image: \( M'(6,9) \), \( N'(15,9) \), \( P'(15,3) \); Type of dilation: Enlargement (since \( k = 3>1 \))