Question

explore translations

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?
4. figure f has vertices with coordinates at (-6, 1), (-3, 1), (-8, 2), (-9, 3), (-6, 3), and (-7, 2). if the figure is translated using the rule (x, y) → (x + 2, y + 5), what are the coordinates of the new vertices?
5. math on the spot graph the translation of △xyz 4 units right and 2 units down.

Explanation:

Problem 4 Solution:

Step 1: Identify the translation rule

The translation rule given 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.

Step 2: Apply the rule to each vertex of Figure F

• For the vertex \((-6, 1)\):
• New \(x\)-coordinate: \(-6 + 2 = -4\)
• New \(y\)-coordinate: \(1 + 5 = 6\)
• New vertex: \((-4, 6)\)
• For the vertex \((-3, 1)\):
• New \(x\)-coordinate: \(-3 + 2 = -1\)
• New \(y\)-coordinate: \(1 + 5 = 6\)
• New vertex: \((-1, 6)\)
• For the vertex \((-8, 2)\):
• New \(x\)-coordinate: \(-8 + 2 = -6\)
• New \(y\)-coordinate: \(2 + 5 = 7\)
• New vertex: \((-6, 7)\)
• For the vertex \((-9, 3)\):
• New \(x\)-coordinate: \(-9 + 2 = -7\)
• New \(y\)-coordinate: \(3 + 5 = 8\)
• New vertex: \((-7, 8)\)
• For the vertex \((-6, 3)\):
• New \(x\)-coordinate: \(-6 + 2 = -4\)
• New \(y\)-coordinate: \(3 + 5 = 8\)
• New vertex: \((-4, 8)\)
• For the vertex \((-7, 2)\):
• New \(x\)-coordinate: \(-7 + 2 = -5\)
• New \(y\)-coordinate: \(2 + 5 = 7\)
• New vertex: \((-5, 7)\)

Answer:

The new coordinates of the vertices are \((-4, 6)\), \((-1, 6)\), \((-6, 7)\), \((-7, 8)\), \((-4, 8)\), and \((-5, 7)\).