Respuesta :
Answer:
pre-image XYZ is X (2, 2), Y (6, 0), Z (1, -1)
Step-by-step explanation:
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A rotation of 90° about the origin includes the interchange of the position of x, and y in the ordered pair and a change of one of the signs of the pair.
The option that shows the pre-image of triangle X'Y'Z' before the figure was rotated 90° about the origin is the option;
- On a coordinate plane, a triangle has points X(2, 2), Y(6, 0), and Z(1, -1).
Reasons:
The given transformation the gives the X'Y'Z' = 90° rotation about the origin
The given coordinates of X'Y'Z' are;
X'(-2, 2), Y'(0, 6), and Z'(1, 1)
Required:
The figure that shows the preimage of X'Y'Z'
Solution:
Given that X'Y'Z' is obtained by the rotation of XYZ 90°, therefore, the
coordinates of XYZ are given by the rotation of X'Y'Z' in the reverse
direction either counterclockwise and clockwise.
(x, y) [tex]\underrightarrow {R_{90^{\circ}}}[/tex] (-y, x)
(x, y) [tex]\underrightarrow {R_{-90^{\circ}}}[/tex] (y, -x)
Therefore, we have;
X'(-2, 2) [tex]\underrightarrow {R_{90^{\circ}}}[/tex] X(-2, -2)
Y'(0, 6) [tex]\underrightarrow {R_{90^{\circ}}}[/tex] Y(-6, 0)
Z'(1, 1) [tex]\underrightarrow {R_{90^{\circ}}}[/tex] Z(-1, 1)
Similarly, we get;
X'(-2, 2) [tex]\underrightarrow {R_{-90^{\circ}}}[/tex] X(2, 2)
Y'(0, 6) [tex]\underrightarrow {R_{-90^{\circ}}}[/tex] Y(6, 0)
Z'(1, 1) [tex]\underrightarrow {R_{-90^{\circ}}}[/tex] Z(1, -1)
The above coordinates of XYZ; X(2, 2), Y(6, 0), and Z(1, -1), corresponds to
the option;
On a coordinate plane, a triangle has points X(2, 2), Y(6, 0), and Z(1, -1).
Therefore, XYZ was rotated 90° clockwise to form X'Y'Z'
Learn more about rotation transformation here:
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