Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4
)? a 180 rotation about the origin a 90 counterclockwise rotation about the origin and a translation down 4 units a 90 clockwise rotation about the origin and a reflection over the y-axis a reflection over the y-axis and then a 90 clockwise rotation about the origin
2 answers:
Notice that every pair of point (x, y) in the original picture, has become (-y, -x) in the transformed figure.
Let ABC be first transformed onto A"B"C" by a 90° clockwise rotation.
Notice that B(4, 1) is mapped onto B''(1, -4). So the rule mapping ABC to A"B"C" is (x, y)→(y, -x)
so we are very close to (-y, -x).
The transformation that maps (y, -x) to (-y, -x) is a reflection with respect to the y-axis. Notice that the 2. coordinate is same, but the first coordinates are opposite.
ANSWER:
"<span>a 90 clockwise rotation about the origin and a reflection over the y-axis</span>"
Let ABC be first transformed onto A"B"C" by a 90° clockwise rotation.
Notice that B(4, 1) is mapped onto B''(1, -4). So the rule mapping ABC to A"B"C" is (x, y)→(y, -x)
so we are very close to (-y, -x).
The transformation that maps (y, -x) to (-y, -x) is a reflection with respect to the y-axis. Notice that the 2. coordinate is same, but the first coordinates are opposite.
ANSWER:
"<span>a 90 clockwise rotation about the origin and a reflection over the y-axis</span>"
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