Question

write a rule to describe each transformation.

1. \\((x, y) \

ightarrow (\quad, \quad)\\)

Explanation:

Identify corresponding vertices

We compare the coordinates of the vertices of figure \(A\) (pre-image) and figure \(B\) (image).

• Top-most vertex of \(A\): \((4, 6)\)
• Corresponding top-most vertex of \(B\): \((2, 3)\)
• Left-most vertex of \(A\): \((1, 5)\)
• Corresponding left-most vertex of \(B\): \((0.5, 2.5)\)
• Bottom-most vertex of \(A\): \((5, 1)\)
• Corresponding bottom-most vertex of \(B\): \((2.5, 0.5)\)
• Right-most vertex of \(A\): \((6, 4)\)
• Corresponding right-most vertex of \(B\): \((3, 2)\)

Calculate the scale factor

We divide the coordinates of the image \(B\) by the coordinates of the pre-image \(A\).
Using the top-most vertex:

$$ k = \frac{2}{4} = 0.5 $$

$$ k = \frac{3}{6} = 0.5 $$

Using the right-most vertex:

$$ k = \frac{3}{6} = 0.5 $$

$$ k = \frac{2}{4} = 0.5 $$

The scale factor is \(0.5\).

Write the transformation rule

A dilation centered at the origin with a scale factor \(k\) has the coordinate rule:

$$ (x, y) ightarrow (kx, ky) $$

Substituting \(k = 0.5\):

$$ (x, y) ightarrow (0.5x, 0.5y) $$

Answer:

Write a rule to describe each transformation.

1. \((x, y)

ightarrow\) <blank>\((0.5x, 0.5y)\)</blank>