Question

problems 1-4

1. translate figure a using the rule (x, y) → (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 c?

Explanation:

Question 2 Solution:

Step1: Identify Coordinates

Find a corresponding vertex of Figure B and Figure D. Let's take the top vertex of Figure B: suppose B's vertex is \((x_1, y_1)\) and D's is \((x_2, y_2)\). From the graph, B's top vertex (approx) is \((-2, -8)\), D's top vertex is \((-8, -2)\).

Step2: Calculate Translation

Change in \(x\): \(x_2 - x_1 = -8 - (-2) = -6\) (so \(x\) decreases by 6, or \(x + (-6)\)). Change in \(y\): \(y_2 - y_1 = -2 - (-8) = 6\) (so \(y\) increases by 6, or \(y + 6\)). Thus, the rule is \((x, y) \to (x - 6, y + 6)\).

A translation moves a figure without rotating, reflecting, or changing its size/shape, only sliding (same direction and distance for all points). Figure E and Figure C: check if all corresponding points have the same horizontal/vertical shift. Figure E appears rotated or has a different orientation/shape relationship (e.g., Figure C is a rectangle, E may be rotated or distorted in a way that translation (pure slide) doesn't account for—translation preserves orientation, E likely has a rotation or reflection component, so it's not a translation.

Answer:

The translation rule from Figure B to Figure D is \(\boldsymbol{(x, y) \to (x - 6, y + 6)}\) (exact coordinates may vary slightly based on graph interpretation, but the direction and magnitude of translation is key: 6 units left and 6 units up).

Question 3 Solution: