Question

1. which sequence correctly describes moving a figure 3 units left, rotating it 90 degrees clockwise, and then reflecting it across the y - axis? a. reflection, rotation, translation b. translation, reflection, rotation c. rotation, translation, reflection d. translation, rotation, reflection 2. if a point at (3, 4) is translated 6 units right and 2 units up, what are its new coordinates? a. (9, 2) b. (6, 2) c. (9, 6) d. (3, 6) 3. which operations can alter the position of a figure on the coordinate plane without changing its orientation? a. reflection b. scaling c. translation d. rotation 4. a rectangle is rotated 90 degrees clockwise around the origin. if one vertex starts at (1, 2), what will be its new coordinates after rotation? a. (1, - 2) b. (2, - 1) c. (2, 1) d. (- 1, 2) 5. how does a dilation affect the size of a figure? a. it reverses b. it becomes infinite

Explanation:

Step1: Analyze question 1

Moving 3 units left is translation, 90 - degree clock - wise rotation is rotation, and reflecting across y - axis is reflection. So the order is translation, rotation, reflection.

Step2: Analyze question 2

For a point (x,y) translated a units right and b units up, the new coordinates are (x + a,y + b). Given (3,4) translated 6 units right and 2 units up, x=3, a = 6, y = 4, b = 2. New x=3 + 6=9, new y=4 + 2=6. New coordinates are (9,6).

Step3: Analyze question 3

Translation moves a figure without changing its orientation. Reflection changes orientation, scaling changes size, and rotation changes orientation.

Step4: Analyze question 4

The rule for a 90 - degree clock - wise rotation around the origin for a point (x,y) is (y,-x). For the point (1,2), new x = 2, new y=-1. New coordinates are (2,-1).

Step5: Analyze question 5

Dilation changes the size of a figure. If the scale factor is greater than 1, it enlarges; if between 0 and 1, it shrinks.

Answer:

1. d. Translation, rotation, reflection
2. c. (9,6)
3. c. Translation
4. b. (2,-1)
5. (No options provided completely in the question for this part. But dilation changes the size of a figure by a scale factor. If scale factor k>1, it enlarges; if 0<k<1, it shrinks)