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. arguments why is figure e not a translation of figure c?
4. figure f has vertices with coordinates at ((-6, 1)), ((-9, 1)), ((-8, 2)), ((-9, 3)), ((-6, 3)), and ((-7, 2)). if the figure is translated using the rule ((x, y) \to (x + 2, y + 5)), what are the coordinates of the new vertices?
5. math on the spot graph the translation of (\triangle xyz) 4 units right and 2 units down.

Explanation:

Problem 4 Solution:

Step1: Identify the translation rule

The translation rule is \((x, y) \to (x + 2, y + 5)\). This means we add 2 to the \(x\)-coordinate and 5 to the \(y\)-coordinate of each vertex.

Step2: Apply the rule to each vertex

• For \((-6, 1)\): \(x=-6 + 2=-4\), \(y = 1+5 = 6\), so the new vertex is \((-4, 6)\).
• For \((-9, 1)\): \(x=-9 + 2=-7\), \(y = 1+5 = 6\), so the new vertex is \((-7, 6)\).
• For \((-8, 2)\): \(x=-8 + 2=-6\), \(y = 2+5 = 7\), so the new vertex is \((-6, 7)\).
• For \((-9, 3)\): \(x=-9 + 2=-7\), \(y = 3+5 = 8\), so the new vertex is \((-7, 8)\).
• For \((-6, 3)\): \(x=-6 + 2=-4\), \(y = 3+5 = 8\), so the new vertex is \((-4, 8)\).
• For \((-7, 2)\): \(x=-7 + 2=-5\), \(y = 2+5 = 7\), so the new vertex is \((-5, 7)\).

Answer:

The new vertices are \((-4, 6)\), \((-7, 6)\), \((-6, 7)\), \((-7, 8)\), \((-4, 8)\), \((-5, 7)\)