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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Answer:
B
Step-by-step explanation:
It isn't A. A has to be something like y = -x^2 That minus sign directs the parabola downward.
It could be B which is something like y = x^3 - 5
C has an odd number of real roots (5). In other words it crosses the x axis 5 times. So let's make one of these up and graph it
y = (x^2 - 4)(x^2 - 1)(x + 3) Study this for a minute. The leading coefficient of this polynomial is plus 1. There are no negatives in front of the x. The highest degree is x^5. Now here's the key question: on the left side where does the graph start? In Quad three right? It's coming from the lower left. That is exactly what graph C is NOT doing. So for C the graph has a leading coefficient that is less than 0. a<0
Not C.
D is not the answer either. It opens downward and looks like it is something like y = - x^4 + 3x^3 - 2x^2 + 5x - 2
Answer B:
