Question

explore translations
use the graph to answer problems 1–4.

1. translate figure a using the rule ((x, y) \to (x + 1, y - 4)). draw the image of figure a. practice reading the rule aloud.
2. how was figure b translated to get figure d? write your answer using mapping notation.
3. construct arguments why is figure e not a translation of figure f?
4. figure f has vertices with coordinates ((-8, 3)), ((-4, 3)), and ((-2, 5)). if the figure is translated using the rule ((x, y) \to (x + 2, y + 1)), what are the coordinates of the new vertices?

Explanation:

Step1: Identify Figure A's coordinates

Assume Figure A has vertices (let's take the diamond) with coordinates, say, (2, 2), (3, 3), (2, 4), (1, 3) (estimating from the graph).

Step2: Apply the translation rule

The rule is \((x, y) \to (x + 1, y - 4)\). So for each vertex:

• For (2, 2): \((2 + 1, 2 - 4) = (3, -2)\)
• For (3, 3): \((3 + 1, 3 - 4) = (4, -1)\)
• For (2, 4): \((2 + 1, 4 - 4) = (3, 0)\)
• For (1, 3): \((1 + 1, 3 - 4) = (2, -1)\)

Step3: Draw the image

Plot these new points (3, -2), (4, -1), (3, 0), (2, -1) and connect them to get the translated figure of A.

Answer:

To translate Figure A using \((x, y) \to (x + 1, y - 4)\), find each vertex of A, apply the rule to get new coordinates, then draw the figure with those new vertices. (The actual drawing would be a diamond shifted 1 unit right and 4 units down from Figure A's position.)