How to Rotate a Shape

Step-by-Step Guide

1. 1

   Step 1: Note the corresponding clockwise and counterclockwise rotations.

   Rotating a shape 90 degrees is the same as rotating it 270 degrees clockwise.The convention is that when rotating shapes on a coordinate plane, they rotate counterclockwise, or towards the left.You should assume this, unless it is noted in the problem that you need to rotate clockwise.
   
   For example, if the problem states, “Rotate the shape 90 degrees around the origin,” you can assume you are rotating the shape counterclockwise.
   
   You would complete this problem the same way you complete a problem that asks “Rotate the shape 270 degrees clockwise around the origin.” You might also see, “Rotate this shape
   -270 degrees around the origin.”
2. 2

   Step 2: Find the coordinates of the original vertices.

   If these aren’t already provided, determine the coordinates using the graph.
   
   Remember that coordinates of points are shown using the (x,y){\displaystyle (x,y)} formula, where x{\displaystyle x} equals the point on the horizontal, or x-axis, and y{\displaystyle y} equals the point on the vertical, or y-axis.
   
   For example, you might have a triangle with points (4, 6), (1, 2), and (1, 8). , The formula is (x,y)→(−y,x){\displaystyle (x,y)\rightarrow (-y,x)}.This formula shows that you are reflecting the shape, then flipping it., Make sure that you keep your x and y-coordinates straight.
   
   In this formula, you take the negative of the y value, and then switch the order of the coordinates.
   
   For example, the points (4, 6), (1, 2), and (1, 8) become (-6, 4), (-2, 1), and (-8, 1). , Plot the new vertex points on the plane.
   
   Connect your points using a straightedge.
   
   The resulting shape shows the original shape rotated 90 degrees around the origin.
3. 3

   Step 3: Set up the formula for rotating a shape 90 degrees.

4. 4

   Step 4: Plug the coordinates into the formula.

5. 5

   Step 5: Draw the new shape.

Detailed Guide

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