What you’ll learn
Perform coordinate dilations.
Key idea
Scale each displacement by the positive factor, then add the center back.
Scale displacement from the center, not absolute coordinates; merged coincident plot labels preserve all roles.
Worked example
Enter the exact value or ordered values in the format requested below.
On this labeled plane O=(-2,-2) is center, P=(-4,-4); dilation factor 1/2. Read the plotted image I coordinate pair.
Marked coordinates: O=(-2, -2); I=(-3, -3); P=(-4, -4).
- For every X use X_image=O+(1/2)(X-O), with O=(-2,-2).
- Original vertices [(-4, -4), (-2, -4), (-4, -2)] give images [(-3, -3), (-2, -3), (-3, -2)]; direct absolute scaling of P would instead give (-2,-2), using the wrong center.
Answer: (-3,-3)
Quick Check
Relate the graph used in 'Perform coordinate dilations' to an equation, table, transformation, or verbal description.
Graph shows center O=(-2,-2), P=(2,-4) and proposed I=(3,-6) for factor 3/2. Connect the plot to a centered coordinate rule and assess whether absolute-coordinate multiplication is valid.
Marked coordinates: O=(-2, -2); P=(2, -4); I=(3, -6).