Question

which transformations would result in a geometric figure that is exactly the same size and shape as \\( \triangle def \\)? check all that apply.
a. rotate \\( \triangle def 90 ^ { \circ } \\) clockwise about the origin.
b. dilate \\( \triangle def \\) by a factor of 3.
c. translate \\( \triangle def \\) three units to the right.
d. reflect \\( \triangle def \\) across the line \\( y = 0 \\).

Explanation:

Step1: Understand the properties of transformations

• Rotation: Rotating a figure (like rotating \(\triangle DEF\) \(90^{\circ}\) clockwise about the origin) is a rigid transformation. Rigid transformations preserve the shape and size of the figure.
• Dilation: Dilating \(\triangle DEF\) by a factor of \(3\) changes the size of the figure. If the scale factor \(k

eq1\), the size of the figure changes (\(k = 3>1\) in this case, so the figure will be enlarged).

• Translation: Translating \(\triangle DEF\) three units to the right is a rigid transformation. Rigid transformations (translations slide the figure without resizing or reshaping) preserve the shape and size of the figure.
• Reflection: Reflecting \(\triangle DEF\) across the line \(y = 0\) (the \(x -\)axis) is a rigid transformation. Rigid transformations preserve the shape and size of the figure.

Answer:

A. Rotate \(\triangle DEF\) \(90^{\circ}\) clockwise about the origin, C. Translate \(\triangle DEF\) three units to the right, D. Reflect \(\triangle DEF\) across the line \(y = 0\)