Coordinate plane rotation worksheet with riddle to solve.

To solve this riddle, we need to find the coordinates of the points after specific rotations and match them to the letters in the table.

Step 1: Identify the original coordinates from the graph.
Looking at the grid:
* Point A is at $(2, 7)$
* Point B is at $(7, 7)$
* Point C is at $(7, 1)$
* Point D is at $(2, 1)$

Step 2: Solve each rotation problem.

1. Find A' after A is rotated $90^\circ$ clockwise.
* Rule for $90^\circ$ clockwise: $(x, y) \rightarrow (y, -x)$
* $A(2, 7) \rightarrow (7, -2)$
* Looking at the table, $(7, -2)$ matches letter A.

2. Find B' after B is rotated $270^\circ$ clockwise.
* Rule for $270^\circ$ clockwise (same as $90^\circ$ counter-clockwise): $(x, y) \rightarrow (-y, x)$
* $B(7, 7) \rightarrow (-7, 7)$
* Looking at the table, $(-7, 7)$ matches letter N.

3. Find C' after C is rotated $180^\circ$ clockwise.
* Rule for $180^\circ$: $(x, y) \rightarrow (-x, -y)$
* $C(7, 1) \rightarrow (-7, -1)$
* Looking at the table, $(-7, -1)$ matches letter O.

4. Find D' after D is rotated $90^\circ$ clockwise.
* Rule for $90^\circ$ clockwise: $(x, y) \rightarrow (y, -x)$
* $D(2, 1) \rightarrow (1, -2)$
* Looking at the table, $(1, -2)$ matches letter T.

5. Find A' after A is rotated $180^\circ$ counter-clockwise.
* Rule for $180^\circ$ (direction doesn't matter for 180): $(x, y) \rightarrow (-x, -y)$
* $A(2, 7) \rightarrow (-2, -7)$
* Looking at the table, $(-2, -7)$ matches letter C.

6. Find B' after B is rotated $270^\circ$ counter-clockwise.
* Rule for $270^\circ$ counter-clockwise (same as $90^\circ$ clockwise): $(x, y) \rightarrow (y, -x)$
* $B(7, 7) \rightarrow (7, -7)$
* Looking at the table, $(7, -7)$ matches letter S.

7. Find C' after C is rotated $90^\circ$ counter-clockwise.
* Rule for $90^\circ$ counter-clockwise: $(x, y) \rightarrow (-y, x)$
* $C(7, 1) \rightarrow (-1, 7)$
* Looking at the table, $(-1, 7)$ matches letter P.

8. Find D' after D is rotated $180^\circ$ counter-clockwise.
* Rule for $180^\circ$: $(x, y) \rightarrow (-x, -y)$
* $D(2, 1) \rightarrow (-2, -1)$
* Looking at the table, $(-2, -1)$ matches letter U.

9. Find A' after A is rotated $270^\circ$ clockwise.
* Rule for $270^\circ$ clockwise: $(x, y) \rightarrow (-y, x)$
* $A(2, 7) \rightarrow (-7, 2)$
* Looking at the table, $(-7, 2)$ matches letter I.

10. Find B' after B is rotated $180^\circ$ clockwise.
* Rule for $180^\circ$: $(x, y) \rightarrow (-x, -y)$
* $B(7, 7) \rightarrow (-7, -7)$
* Looking at the table, $(-7, -7)$ matches letter B.

11. Find C' after C is rotated $90^\circ$ clockwise.
* Rule for $90^\circ$ clockwise: $(x, y) \rightarrow (y, -x)$
* $C(7, 1) \rightarrow (1, -7)$
* Looking at the table, $(1, -7)$ matches letter L.

12. Find D' after D is rotated $90^\circ$ counter-clockwise.
* Rule for $90^\circ$ counter-clockwise: $(x, y) \rightarrow (-y, x)$
* $D(2, 1) \rightarrow (-1, 2)$
* Looking at the table, $(-1, 2)$ matches letter E.

Step 3: Assemble the message.
The numbers at the bottom correspond to the question numbers. Let's put the letters in order:

10: B
12: E
5: C
1: A
8: U
6: S
12: E
9: I
4: T
4: T
6: S
7: P
3: O
2: N
4: T
6: S

The phrase spells out: BECAUSE IT TSPO NTS? Wait, let me re-check the number sequence at the very bottom.
The numbers are: `10 12 5 1 8 6 12 9 4 4 6 7 3 9 2 4 11 12 6 6`

Let's map them again carefully:
10 -> B
12 -> E
5 -> C
1 -> A
8 -> U
6 -> S
12 -> E
9 -> I
4 -> T
4 -> T
6 -> S
7 -> P
3 -> O
9 -> I
2 -> N
4 -> T
11 -> L
12 -> E
6 -> S
6 -> S

The sentence is: BECAUSE IT TS POINTLESS

Wait, looking at indices 8, 9, 10, 11 in the sequence `... 8 6 12 9 4 4 6 ...`
Index 8 in sentence is letter from Q6 (S)
Index 9 in sentence is letter from Q12 (E)
Index 10 in sentence is letter from Q9 (I)
Index 11 in sentence is letter from Q4 (T)
Index 12 in sentence is letter from Q4 (T)
Index 13 in sentence is letter from Q6 (S)

So "IT" is followed by "SETTS"? No.
Let's look at the words:
B E C A U S E (Because)
I T (It)
S P O I N T L E S S (Pointless?? No, S is before P).

Let's re-read the sequence `9 4 4 6 7 3 9 2 4 11 12 6 6`.
9 -> I
4 -> T
4 -> T
6 -> S
7 -> P
3 -> O
9 -> I
2 -> N
4 -> T
11 -> L
12 -> E
6 -> S
6 -> S

This spells: IT TSPOINTLESS. That doesn't make sense. The joke is usually "Why does nobody talk to circles? Because it's pointless."

Let's check Question 6 again.
Q6: Find B' after B is rotated $270^\circ$ counter-clockwise.
$B(7,7) \rightarrow (7, -7)$. Letter S. Correct.

Let's check Question 12 again.
Q12: Find D' after D is rotated $90^\circ$ counter-clockwise.
$D(2,1) \rightarrow (-1, 2)$. Letter E. Correct.

Let's check Question 9 again.
Q9: Find A' after A is rotated $270^\circ$ clockwise.
$A(2,7) \rightarrow (-7, 2)$. Letter I. Correct.

Let's check Question 4 again.
Q4: Find D' after D is rotated $90^\circ$ clockwise.
$D(2,1) \rightarrow (1, -2)$. Letter T. Correct.

Let's check Question 7 again.
Q7: Find C' after C is rotated $90^\circ$ counter-clockwise.
$C(7,1) \rightarrow (-1, 7)$. Letter P. Correct.

Let's check Question 3 again.
Q3: Find C' after C is rotated $180^\circ$ clockwise.
$C(7,1) \rightarrow (-7, -1)$. Letter O. Correct.

Let's check Question 2 again.
Q2: Find B' after B is rotated $270^\circ$ clockwise.
$B(7,7) \rightarrow (-7, 7)$. Letter N. Correct.

Let's check Question 11 again.
Q11: Find C' after C is rotated $90^\circ$ clockwise.
$C(7,1) \rightarrow (1, -7)$. Letter L. Correct.

The sequence at the bottom is:
`10 12 5 1 8 6 12` -> B E C A U S E
`9 4` -> I T
`4 6 7 3 9 2 4 11 12 6 6` -> T S P O I N T L E S S

Ah, I see. The word is POINTLESS, but there is an extra TS before it?
Let's look at the numbers again: `... 9 4 4 6 7 ...`
9=I, 4=T. So we have "IT".
Then `4 6 7 ...` -> T, S, P.
So it says "IT TS POINTLESS".

Is it possible Q4 or Q6 is different?
Q4: D(2,1) rot 90 CW -> (1,-2). Table: T is (1,-2). Correct.
Q6: B(7,7) rot 270 CCW -> (7,-7). Table: S is (7,-7). Correct.

Maybe the joke is "Because it's pointless" and the "TS" is a typo in my reading or the worksheet?
Let's look at the number string very closely in the image.
`10 12 5 1 8 6 12` (BECAUSE)
`9 4` (IT) -- Wait, is that a 9 and a 4? Yes.
Then `4 6`? Or is it `1 4`?
If it were `1 4`, 1=A, 4=T. "AT". No.
If it were `5 4`, 5=C, 4=T. "CT". No.

Let's look at the standard joke: "Why does nobody talk to circles? Because it's pointless."
"It's" = I T ' S.
We have I (9), T (4). We need an apostrophe S.
The next numbers are 4, 6.
4 is T. 6 is S.
So we have I T T S.
Then 7 (P) 3 (O) 9 (I) 2 (N) 4 (T) 11 (L) 12 (E) 6 (S) 6 (S).
This spells IT TSPOINTLESS.

Actually, looking at the spacing in the numbers:
`10 12 5 1 8 6 12`
`9 4`
`4 6` ?? Maybe the first 4 is actually part of the previous word? No.
Is it possible Q4 is not T?
D(2,1) -> 90 CW -> (1, -2).
Table: T is (1, -2). It is definitely T.

Is it possible Q6 is not S?
B(7,7) -> 270 CCW -> (7, -7).
Table: S is (7, -7). It is definitely S.

Perhaps the intended answer ignores the extra letters or interprets "IT TS" as "IT'S"?
"I" (9)
"T" (4)
"S" (6) -- If the sequence was 9, 4, 6... it would be ITS.
But the sequence is 9, 4, 4, 6...
There is an extra 4 (T).

However, the punchline is clearly BECAUSE IT'S POINTLESS. Even if there is a typo in the worksheet's number key (an extra 4), the answer to the riddle is the standard joke.

Final Answer:
BECAUSE IT'S POINTLESS