A rigid transformation is one in which the distance between pairs of points
are preserved, and the image and preimage have the same dimensions.
- The transformations that will produce an image that is congruent to the given figure is; Number 1 and 2.
Reasons:
The vertices of the trapezoid GHIZ are G(0, 0), H(-1, 2), I(3, 2), and J(2, 0)
The given transformations are;
1. GHIJ is reflected in the x-axis and the image is reflected in the y-axis
The above transformation is a double reflection.
2. GHIJ is rotated about the origin 90° counterclockwise. The resulting
image is translated up 2 units.
3. GHIJ is dilated by a scale factor of [tex]\mathbf{\frac{1}{2}}[/tex], with the center of dilation at the
origin. The resulting image is translated 2 units left.
Required:
The transformations that produce an image that is congruent to the given figure:
Solution:
Two figures are congruent if they have the same size and shape.
With the given figure being the trapezoid GHIJ, we have that a
transformation that will give an image that is congruent to the preimage
which is the trapezoid GHIJ is a rigid transformation.
Rigid transformations are;
The combinations of transformation given within the scenario that consists
of only rigid transformations are scenario 1 and scenario 2.
Therefore, the correct option is; Numbers 1 and 2.
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