Respuesta :
Answer:
(x,y) → (y,-x)
Step-by-step explanation:
We are given two parallelograms.
ABCD with coordinates
A=(2,5)
B=(5,4)
C=(5,2)
D=(2,3)
Another parallelogram A'B'C'D' with coordinates
A'=(5,-2)
B'=(4,-5)
C'=(2,-5)
D'=(3,-2)
Now, A is transformed to A' that is (2,5) is transformed to (5,-2)
We see that the y coordinate becomes the x-coordinate after transformation and the negative of x coordinates becomes y coordinate after transformation.
A similar pattern can be seen for the B, C and D.
Thus, the transformation is given by:
(x,y) → (y,-x)
A translation transformation is a transformation in which all the points on an object are translated in the same direction
The rule that describes the transformation of parallelogram ABCD to parallelogram A'B'C'D' is (x, y) → (y, -x)
The reasons the above selection is correct are as follows;
The coordinates of the vertices of the parallelogram ABCD are;
A(2, 5) , B(5, 4), C(5, 2), and D(2, 3)
The coordinates of the vertices of the parallelogram A'B'C'D' are;
A'(5, -2), B'(4, -5), C'(2, -5), and D'(3, -2)
Required:
To select the rule that determines the transformation
Solution:
By observation, we have;
The x-coordinate and y-coordinate values of the parallelogram ABCD are the same as the y-coordinate and negative x-coordinate values of parallelogram A'B'C'D', respectively
Therefore the rule that describes the transformation is (x, y) → (y, -x)
Which gives;
A(2, 5) [tex]\underset \longrightarrow {(x, \ y) \rightarrow (y, \ -x)}[/tex] A'(5, -2)
B(5, 4) [tex]\underset \longrightarrow {(x, \ y) \rightarrow (y, \ -x)}[/tex] B'(4, -5)
C(5, 2) [tex]\underset \longrightarrow {(x, \ y) \rightarrow (y, \ -x)}[/tex] C'(2, -5)
D(2, 3) [tex]\underset \longrightarrow {(x, \ y) \rightarrow (y, \ -x)}[/tex] D'(3, -2)
The correct option for the rule is (x, y) → (y, -x)
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