Example Question - counterclockwise rotation
Here are examples of questions we've helped users solve.
Rotating Points Around the Origin
To solve the question in the image, we need to determine the new positions of the vertices after a 270° counterclockwise rotation around the origin. The original coordinates of the vertices appear to be: - J(6,3) - K(9,3) - L(6,-2) Here are the general rules for rotating points around the origin: - For a 90° counterclockwise rotation, (x, y) becomes (-y, x). - For a 180° rotation, (x, y) becomes (-x, -y). - For a 270° counterclockwise rotation, (x, y) becomes (y, -x). Applying the rule for a 270° rotation to each point: For J(6,3): Rotate 270° counterclockwise to get J'(3,-6). For K(9,3): Rotate 270° counterclockwise to get K'(3,-9). For L(6,-2): Rotate 270° counterclockwise to get L'(-2,-6). Therefore, the new coordinates after the 270° counterclockwise rotation around the origin are: - J'(3, -6) - K'(3, -9) - L'(-2, -6)
Coordinate Plane 90-Degree Rotation
To perform a 90-degree counterclockwise rotation around the origin on a coordinate plane, you can use the following rule: If the original point is (x, y), the coordinates after a 90-degree counterclockwise rotation will be (-y, x). Now let's apply this rule to the vertices of the figure: - For point R (at approximately -7, -3), after rotation it will become (3, -7). - For point S (at approximately -2, -3), after rotation it will become (3, -2). - For point T (at approximately -2, -8), after rotation it will become (8, -2). - For point Q (at approximately -7, -8), after rotation it will become (8, -7). Please verify the exact coordinates on the graph as they could be slightly different from the estimates I provided based on the image.
Calculating 180-Degree Rotation of a Point
To solve the question, we need to rotate the point N (√3, 5) by 180 degrees counterclockwise around the origin. When rotating a point 180 degrees either clockwise or counterclockwise around the origin (0,0), the coordinates of the point are essentially negated. This results in the point (x, y) becoming (-x, -y). So, for the point N (√3, 5), the new coordinates after a 180-degree rotation will be (-√3, -5). Thus, the coordinates of the resulting point, N', are (-√3, -5).
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