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: Translate each vertex

• For \((-6, 1)\):

New \(x\): \(-6 + 2 = -4\)
New \(y\): \(1 + 5 = 6\)
New coordinate: \((-4, 6)\)

• For \((-9, 1)\):

New \(x\): \(-9 + 2 = -7\)
New \(y\): \(1 + 5 = 6\)
New coordinate: \((-7, 6)\)

• For \((-8, 2)\):

New \(x\): \(-8 + 2 = -6\)
New \(y\): \(2 + 5 = 7\)
New coordinate: \((-6, 7)\)

• For \((-9, 3)\):

New \(x\): \(-9 + 2 = -7\)
New \(y\): \(3 + 5 = 8\)
New coordinate: \((-7, 8)\)

• For \((-6, 3)\):

New \(x\): \(-6 + 2 = -4\)
New \(y\): \(3 + 5 = 8\)
New coordinate: \((-4, 8)\)

• For \((-7, 2)\):

New \(x\): \(-7 + 2 = -5\)
New \(y\): \(2 + 5 = 7\)
New coordinate: \((-5, 7)\)

Answer:

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