Question

which transformations do not alter the orientation of a figure?
a. translation
b. shearing
c. rotation
d. reflection

after a 180-degree rotation about the origin, what happens to the coordinates of any point (x, y)?
a. (-y, -x)
b. (-x, -y)
c. (y, x)
d. (x, -y)

if a point at (3, 4) is translated 6 units right and 2 units up, what are its new coordinates?
a. (9, 2)
b. (3, 6)
c. (9, 6)
d. (6, 2)

which sequences of transformations could be used to mirror a landscape design from its original plan?
a. reflect across the property’s central line
b. dilation to fit scale adjustments
c. rotate to match terrain variations
d. translate to adjust position within boundaries

Explanation:

First Question:

Translation (sliding) and rotation (turning around a point) preserve orientation. Shearing and reflection (flipping) change orientation. So translation (a) and rotation (c) don't alter orientation. But if choosing one, translation is a primary orientation - preserving transformation.

Step1: Recall 180 - degree rotation rule

For a point \((x,y)\) rotated 180 degrees about the origin, the rule is \((x,y)\to(-x,-y)\).

Step1: Translate x - coordinate

Moving right 6 units: \(3 + 6=9\).

Step2: Translate y - coordinate

Moving up 2 units: \(4 + 2 = 6\).

Answer:

a. Translation, c. Rotation

Second Question: