1.True or false: The mapping notation for reflecting point (x, y) about the x-axis is (−x,y).
A. This statement is false. The mapping notation for reflecting point (x,y) about the x-axis is (y,x).
B. This statement is true.
C. This statement is false. The mapping notation for reflecting point (x,y) about the x�-axis is (−x,−y)
D. This statement is false. The mapping notation for reflecting point (x,y) about the x�-axis is (x,−y).
2. What is the mapping notation for translating point (x,y) down 3 units?
A. (x,y−3)
B. (x+3,y)
C. (x,y+3)
D. (x−3,y)
3. What translation vector translates A(−2,7) to A′(5,−1)?
A. (−7,8)
B. (7,−8)
C. (3,6)
D. (3,−6)
4. Which transformation maps B(2,5) to B′(−2,−5)?
A. A 180° rotation
B. A °270° rotation
C. A °90° rotation
D. Reflection about the y-axis
5. Point (a,b) is reflected about the x-axis. The resulting point is then reflected about the y-axis to produce a final point. Which transformation maps the original point directly to the final
A. A °270° rotation
B. A°90° rotation
C. A°180° rotation
D. A translation down b units and to the left a units
1. False. The mapping notation for reflecting point (x,y) about the x-axis is (x,-y).
2. (x,y-3)
3. (7,-8)
4. Reflection about the y-axis
5. A 180° rotation
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1. True or false: The mapping notation for reflecting point (x, y) about the x-axis is (−x, y).
C. This statement is false. The correct mapping notation for reflecting a point (x, y) about the x-axis is (x, -y). To visualize this, you can imagine flipping the point across the x-axis while keeping the x-coordinate unchanged.
2. What is the mapping notation for translating point (x, y) down 3 units?
A. (x, y - 3)
To perform a translation down 3 units, you need to subtract 3 from the y-coordinate while keeping the x-coordinate unchanged. Therefore, the correct mapping notation is (x, y - 3).
3. What translation vector translates A(-2, 7) to A'(5, -1)?
D. (3, -6)
To find the translation vector, subtract the corresponding coordinates of point A' from point A. This gives us (5 - (-2), -1 - 7) = (7, -8). Therefore, the translation vector is (7, -8).
4. Which transformation maps B(2, 5) to B'(-2, -5)?
D. Reflection about the y-axis
To map B(2, 5) to B'(-2, -5), you need to perform a reflection about the y-axis. This means that the x-coordinate of B is negated to get the x-coordinate of B', while the y-coordinate remains the same, resulting in B'(-2, -5).
5. Point (a, b) is reflected about the x-axis. The resulting point is then reflected about the y-axis to produce a final point. Which transformation maps the original point directly to the final point?
C. A°180° rotation
If you reflect a point about the x-axis, the x-coordinate remains the same, but the sign of the y-coordinate is reversed. If you reflect this point about the y-axis, the y-coordinate remains the same, but the sign of the x-coordinate is reversed. Therefore, reflecting a point about the x-axis and then about the y-axis is equivalent to rotating the point 180 degrees counterclockwise, resulting in the original point.