QUESTION IMAGE
Question
transformation summative activity chart
labeled point\tpre - image\ttranslation\treflection\trotation\tbonus: dilation
rule:\t\t$(x + 6, y + 2)$\t\t\t
a\t$(3, 14)$\t\t\t\t
b\t$(8, 19)$\t\t\t\t
c\t$(14, 14)$\t\t\t\t
d\t$(5, 14)$\t\t\t\t
e\t$(5, 10)$\t\t\t\t
f\t$(5, 6)$\t\t\t\t
g\t$(3, 7)$\t\t\t\t
h\t$(3, 10)$\t\t\t\t
i\t$(3, 12)$\t\t\t\t
j\t$(14, 12)$\t\t\t\t
To solve the translation for each labeled point, we use the translation rule \((x + 6, y + 2)\). We will apply this rule to each pre - image point.
Step 1: For point A \((3,14)\)
We substitute \(x = 3\) and \(y = 14\) into the translation rule \((x+6,y + 2)\).
For the \(x\) - coordinate: \(x+6=3 + 6=9\)
For the \(y\) - coordinate: \(y + 2=14+2 = 16\)
So the translated point for A is \((9,16)\)
Step 2: For point B \((8,19)\)
Substitute \(x = 8\) and \(y=19\) into the rule \((x + 6,y+2)\)
\(x\) - coordinate: \(x + 6=8+6 = 14\)
\(y\) - coordinate: \(y + 2=19+2=21\)
Translated point for B is \((14,21)\)
Step 3: For point C \((14,14)\)
Substitute \(x = 14\) and \(y = 14\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=14 + 6=20\)
\(y\) - coordinate: \(y + 2=14+2 = 16\)
Translated point for C is \((20,16)\)
Step 4: For point D \((5,14)\)
Substitute \(x = 5\) and \(y = 14\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=5+6 = 11\)
\(y\) - coordinate: \(y + 2=14+2=16\)
Translated point for D is \((11,16)\)
Step 5: For point E \((5,10)\)
Substitute \(x = 5\) and \(y = 10\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=5 + 6=11\)
\(y\) - coordinate: \(y+2=10 + 2=12\)
Translated point for E is \((11,12)\)
Step 6: For point F \((5,6)\)
Substitute \(x = 5\) and \(y = 6\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=5+6 = 11\)
\(y\) - coordinate: \(y + 2=6+2=8\)
Translated point for F is \((11,8)\)
Step 7: For point G \((3,7)\)
Substitute \(x = 3\) and \(y = 7\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=3+6 = 9\)
\(y\) - coordinate: \(y + 2=7+2=9\)
Translated point for G is \((9,9)\)
Step 8: For point H \((3,10)\)
Substitute \(x = 3\) and \(y = 10\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=3+6 = 9\)
\(y\) - coordinate: \(y + 2=10+2=12\)
Translated point for H is \((9,12)\)
Step 9: For point I \((3,12)\)
Substitute \(x = 3\) and \(y = 12\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=3+6 = 9\)
\(y\) - coordinate: \(y + 2=12+2=14\)
Translated point for I is \((9,14)\)
Step 10: For point J \((14,12)\)
Substitute \(x = 14\) and \(y = 12\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=14+6 = 20\)
\(y\) - coordinate: \(y + 2=12+2=14\)
Translated point for J is \((20,14)\)
If we want to present the results in a table:
| Labeled Point | Pre - image | Translation |
|---|---|---|
| B | \((8,19)\) | \((14,21)\) |
| C | \((14,14)\) | \((20,16)\) |
| D | \((5,14)\) | \((11,16)\) |
| E | \((5,10)\) | \((11,12)\) |
| F | \((5,6)\) | \((11,8)\) |
| G | \((3,7)\) | \((9,9)\) |
| H | \((3,10)\) | \((9,12)\) |
| I | \((3,12)\) | \((9,14)\) |
| J | \((14,12)\) | \((20,14)\) |
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To solve the translation for each labeled point, we use the translation rule \((x + 6, y + 2)\). We will apply this rule to each pre - image point.
Step 1: For point A \((3,14)\)
We substitute \(x = 3\) and \(y = 14\) into the translation rule \((x+6,y + 2)\).
For the \(x\) - coordinate: \(x+6=3 + 6=9\)
For the \(y\) - coordinate: \(y + 2=14+2 = 16\)
So the translated point for A is \((9,16)\)
Step 2: For point B \((8,19)\)
Substitute \(x = 8\) and \(y=19\) into the rule \((x + 6,y+2)\)
\(x\) - coordinate: \(x + 6=8+6 = 14\)
\(y\) - coordinate: \(y + 2=19+2=21\)
Translated point for B is \((14,21)\)
Step 3: For point C \((14,14)\)
Substitute \(x = 14\) and \(y = 14\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=14 + 6=20\)
\(y\) - coordinate: \(y + 2=14+2 = 16\)
Translated point for C is \((20,16)\)
Step 4: For point D \((5,14)\)
Substitute \(x = 5\) and \(y = 14\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=5+6 = 11\)
\(y\) - coordinate: \(y + 2=14+2=16\)
Translated point for D is \((11,16)\)
Step 5: For point E \((5,10)\)
Substitute \(x = 5\) and \(y = 10\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=5 + 6=11\)
\(y\) - coordinate: \(y+2=10 + 2=12\)
Translated point for E is \((11,12)\)
Step 6: For point F \((5,6)\)
Substitute \(x = 5\) and \(y = 6\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=5+6 = 11\)
\(y\) - coordinate: \(y + 2=6+2=8\)
Translated point for F is \((11,8)\)
Step 7: For point G \((3,7)\)
Substitute \(x = 3\) and \(y = 7\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=3+6 = 9\)
\(y\) - coordinate: \(y + 2=7+2=9\)
Translated point for G is \((9,9)\)
Step 8: For point H \((3,10)\)
Substitute \(x = 3\) and \(y = 10\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=3+6 = 9\)
\(y\) - coordinate: \(y + 2=10+2=12\)
Translated point for H is \((9,12)\)
Step 9: For point I \((3,12)\)
Substitute \(x = 3\) and \(y = 12\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=3+6 = 9\)
\(y\) - coordinate: \(y + 2=12+2=14\)
Translated point for I is \((9,14)\)
Step 10: For point J \((14,12)\)
Substitute \(x = 14\) and \(y = 12\) into \((x + 6,y+2)\)
\(x\) - coordinate: \(x+6=14+6 = 20\)
\(y\) - coordinate: \(y + 2=12+2=14\)
Translated point for J is \((20,14)\)
If we want to present the results in a table:
| Labeled Point | Pre - image | Translation |
|---|---|---|
| B | \((8,19)\) | \((14,21)\) |
| C | \((14,14)\) | \((20,16)\) |
| D | \((5,14)\) | \((11,16)\) |
| E | \((5,10)\) | \((11,12)\) |
| F | \((5,6)\) | \((11,8)\) |
| G | \((3,7)\) | \((9,9)\) |
| H | \((3,10)\) | \((9,12)\) |
| I | \((3,12)\) | \((9,14)\) |
| J | \((14,12)\) | \((20,14)\) |