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Sample Question 5:
Step 1: The final image of is . We know the reflection rule for reflecting over is . So before the reflection and after rotation, the point is .
Step 2: By definition of rotation, the slope between and must be perpendicular to the slope between and . The first slope is . This means the slope of and is .
Step 3: Rotations also preserve distance to the center of rotation, and since we only "travelled" up and down by the slope once to get from to it follows we shall only use the slope once to travel from to .
Step 4: Therefore point is located at . The answer is , so the correct answer choice is .
The point in the -plane is first rotated counterclockwise by around the point and then reflected about the line . The image of after these two transformations is at . What is
Answer Keys
Question 5: DSolutions
Question 5Step 1: The final image of is . We know the reflection rule for reflecting over is . So before the reflection and after rotation, the point is .
Step 2: By definition of rotation, the slope between and must be perpendicular to the slope between and . The first slope is . This means the slope of and is .
Step 3: Rotations also preserve distance to the center of rotation, and since we only "travelled" up and down by the slope once to get from to it follows we shall only use the slope once to travel from to .
Step 4: Therefore point is located at . The answer is , so the correct answer choice is .