Let's solve this step by step.

The### Step problem involves a1 geometric transformation:: Identify rotating a the point 270° original clockwise point about theFrom origin the.

graph### Steps, to the solve: marked1 point in the. ** original figureIdentify the original point is's located coordinates** at: : Look at$the(-5, graph - and2). find$

the### coordinates Step of 2 the: Rotation marked point of in the270° original clockwise about figure the.

origin 2.When Apply a the point270° clockwise \ rotation formula((: x, y)) The is formula rotated to 270 rotate° a clockwise point around \ the(( originx, y)) ,270 the° clockwise is transformation: is given by : [ \ ([ x(x,, y y)) \ \to (-toy, x (). ]

y### Apply, - thex transformation) : ] Sub This transforms the originalstit coordinates into the final coordinatesuting ((-.

5, -32. Write)) into the the formula: \ final coordinates[ (-: After5 applying the rotation,, record the new position of the point.

Let - me2) \to extract (-(- the coordinates of2), the - point from the5) image to proceed =. (2, -5). ]

Step 3: Final Result

• Original Point: $(-5, -2)$
• Final Point after Rotation: $(2, -5)$

Let me know if you'd like a breakdownFrom of the these image, steps the marked or point in the additional original details figure!

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at **####(- 45, Related - Questions2: )**1.

.### What Applying happens the to the coordinates270 if the rotation° was Clock wise90 Rotation° counterclockwise instead? 2 Formula: . HowTo rotate does the transformation formula for 180° the rotation point differ \ from((-4 ,270° -? 23.)\ What) is the270 geometric° significance clockwise of about270° the clockwise rotation origin? , use the formula4. How: do you$$determine(x if, y the rotation) is clockwise \to (y or counterclock, -wise fromx) the transformation formulas? 5.\ How]

Substitute can: [ (- you use a matrix to represent the rotation process?

Tip:

Always double4, -2) \to (-2-check, 4)$$

Results:

• the direction of rotation Point (clockwise or counterclock in originalwise figure) to: ensure \ you're applying the((- correct transformation formula!4, -2))
• Point in final figure: $(-2, 4)$

Would you like a detailed breakdown of this transformation or further clarification?

Related Questions:

1. What is the formula for a 90° clockwise rotation about the origin?
2. How does a 270° clockwise rotation compare to a 90° counterclockwise rotation?
3. What happens to the point $(4, 5)$ if it is rotated 270° clockwise about the origin?
4. How can you verify the correctness of a rotation using graphing tools?
5. Can you describe the geometric significance of rotating shapes about the origin?

Tip:

Remember, a 270° clockwise rotation is equivalent to a 90° counterclockwise rotation. This equivalence can simplify solving some problems.