Question

1. select all of the following transformations that result in figures with congruent angles but not congruent sides.

a. (3x, 3y)
b. (-x, -y)
c. (x + 9, y - 1)
d. (1/2x, 1/2y)
e. (-y, x)
f. (-x, y)
g. (y, -x)
h. (4x, 2y)

Explanation:

Step1: Analyze each transformation

• a. \((3x,3y)\):

This is a dilation with a scale factor of \(3\). Dilation preserves angle measures (so angles are congruent) but changes side lengths (so sides are not congruent).

• b. \((-x,-y)\):

This is a rotation of \(180^{\circ}\) about the origin. Rotation is a rigid transformation. Rigid transformations preserve both angle measures and side lengths.

• c. \((x + 9,y-1)\):

This is a translation. Translation is a rigid transformation. Rigid transformations preserve both angle measures and side lengths.

• d. \((\frac{1}{2}x,\frac{1}{2}y)\):

This is a dilation with a scale factor of \(\frac{1}{2}\). Dilation preserves angle measures (so angles are congruent) but changes side lengths (so sides are not congruent).

• e. \((-y,x)\):

This is a rotation of \(90^{\circ}\) counter - clockwise about the origin. Rotation is a rigid transformation. Rigid transformations preserve both angle measures and side lengths.

• f. \((-x,y)\):

This is a reflection over the \(y\) - axis. Reflection is a rigid transformation. Rigid transformations preserve both angle measures and side lengths.

• g. \((y,-x)\):

This is a rotation of \(270^{\circ}\) counter - clockwise about the origin. Rotation is a rigid transformation. Rigid transformations preserve both angle measures and side lengths.

• h. \((4x,2y)\):

This is a non - uniform dilation. For a non - uniform dilation (where the scale factor for \(x\) and \(y\) are different), angle measures are preserved (because the shape is still similar in terms of angles) but side lengths are not congruent (since the scaling is not the same in both \(x\) and \(y\) directions).

Answer:

A. \((3x,3y)\), D. \((\frac{1}{2}x,\frac{1}{2}y)\), H. \((4x,2y)\)