Virginia SOL 7.MG.4

7.MG.4 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 7.MG.4.a

  Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been dilated. Scale factors are limited to 1 4 , 1 2 , 2, ...

• 7.MG.4.b

  Sketch the image of a dilation of a polygon limited to a scale factor of 1 4 , 1 2 , 2, 3, or 4. The center of the dilation will be the origin.

• 7.MG.4.c

  Identify and describe dilations in context including, but not limited to, scale drawings and graphic design.

01

What Students Need to Do

Students multiply both coordinates of every polygon vertex by a given scale factor. They plot the new vertices, sketch the image, and connect dilation to scale drawings or resized graphics.

02

What Mastery Looks Like

Students correctly multiply each x-coordinate and y-coordinate by the scale factor, then plot and connect the image points. They explain that lengths change proportionally while angle measures and overall shape stay the same.

03

Common Misconceptions

Students may add the scale factor to each coordinate instead of multiplying. They may reverse x and y, mishandle negative coordinates, or think a smaller scale factor changes the polygon’s shape.

04

How to Assess It

Give students triangle A(2, 4), B(6, 2), and C(-2, 2). Ask them to find and plot its image after a dilation by 1/2 about the origin.

1. 01

   Plot a masking-tape polygon on a floor grid, then move each vertex using a scale factor of 2 from the origin.

2. 02

   Ask students to explain why multiplying only the x-coordinates does not produce a dilation centered at the origin.

3. 03

   Play coordinate relay: teams draw a card showing 1/4, 1/2, 2, 3, or 4 and calculate one image vertex.

4. 04

   Give students a simple logo on a coordinate grid and have them create enlarged and reduced versions for two sign sizes.

• 3.MG.4

  The student will identify, describe, classify, compare, combine, and subdivide polygons. 

• 6.MG.4

  The student will determine congruence of segments, angles, and polygons.

• 8.MG.3

  The student will apply translations and reflections to polygons in the coordinate plane.