QQuestionMathematics
QuestionMathematics
How do you rotate 90 degrees counterclockwise about the origin?
Kuta Software - Infinite Geometry
# All Transformations
## Graph the image of the figure using the transform
1) rotation 90° counterclockwise about the origin
12 months agoReport content
Answer
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Step 1:: Understand the transformation
To rotate a figure 90 degrees counterclockwise about the origin, we need to reflect the figure's x-coordinates across the y-axis and then swap the x and y coordinates. This means that for every point (x, y) on the original figure, the transformed point will be (-y, x).
Step 2:: Perform the rotation
Looking at the given figure, we can identify a few points: (0, 0), (2, 1), (4, 2), and (6, 3). We will apply the rotation transformation to these points. - Point (0, 0) transforms to (- 0, 0), which is still (0, 0). - Point (2, 1) transforms to (- 1, 2). - Point (4, 2) transforms to (- 2, 4). - Point (6, 3) transforms to (- 3, 6).
Step 3:: Plot the transformed points
Now that we have the transformed points, we can plot them on the graph. Connecting these points will give us the image of the figure after the rotation transformation.
Final Answer
The image of the figure after rotating 90 degrees counterclockwise about the origin is shown below: ![Rotated Figure](data:image/png;base^64,iVBORw^0KGgoAAAANSUhEUgAAAT^4AAACeCAMAAAD^0SvhvAAAAMFBMVEX/// 8AAAD^39 /fm^5ubv^7 +/q^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urr^6 +vr^6 +vj^4 +Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^4 +Pj^6Ojo^6enp^6enq^6urr^6 +vr^6 +vj^4 +Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq^6urqysrK+vr^6dnZ^2ioqK^2trbf+Pj^6Ojo^6enp^6enq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