Question

directions: answer each question. use your answer to find the color. use the color on the corresponding numbers on the picture.

1. a figure is transformed using the rule (x, y)→(x - 3, y). which answer correctly describes this transformation?
2. a figure is transformed using the rule (x, y)→(-x, -y). which answer correctly describes this transformation?
3. a figure is transformed using the rule (x, y)→(4x, 4y). which answer correctly describes this transformation?

ccw = counterclockwise
*sf = scale factor
translation left 3 pink, translation down 3 blue, translation right 3 yellow, rotation 270° ccw pink, rotation 90° ccw orange, rotation 180° ccw purple, translation up 4 purple, dilation sf = 4 orange, translation down 4 blue

1. triangle abc is reflected across the x - axis. which algebraic rule represents a point (x, y) on triangle abc?
2. triangle abc is rotated 270° counterclockwise about the origin. which algebraic rule represents a point (x, y) on triangle abc?
3. triangle abc is translated 2 units up. which algebraic rule represents a point (x, y) on triangle abc?

(x, -y) lime green, (-x, -y) yellow, (-x, y) orange, (-y, x) purple, (y, -x) yellow, (y, x) pink, (x, y - 2) lime green, (x + 2, y) blue, (x, y + 2) purple

1. which algebraic rule represents the transformation shown on the grid?
2. which algebraic rule represents the transformation shown on the grid?
3. which algebraic rule represents the transformation shown on the grid?

(x - 2, y - 2) yellow, (2x, 2y) orange, (0.5x, 0.5y) pink, (-x, y) purple, (x + 4, y) lime green, (x, -y) blue, (x - 6, y + 6) purple, (x + 6, y - 6) pink, (-x, -y) orange

1. which algebraic rule represents the transformation shown on the grid?
2. which algebraic rule represents the transformation shown on the grid?
3. which algebraic rule represents the transformation shown on the grid?

(y, -x) orange, (-y, x) pink, (-x, y) blue, (2/3x, 2/3y) yellow, (3x, 2y) purple, (1.5x, 1.5y) lime green, (x, y - 6) light blue, (x - 6, y) pink, (x, y + 6) orange

Explanation:

Step1: Analyze rule (x,y)→(x - 3,y)

Moving x - coordinate 3 units left is translation left 3.

Step2: Analyze rule (x,y)→(-x,-y)

This is 180° counter - clockwise rotation about origin.

Step3: Analyze rule (x,y)→(4x,4y)

Multiply both coordinates by 4, it's dilation with scale factor 4.

Step4: Reflecting across x - axis

The y - coordinate changes sign, rule is (x, -y).

Step5: Rotate 270° counter - clockwise about origin

The rule for 270° CCW rotation is (-y, x).

Step6: Translate 2 units up

Add 2 to y - coordinate, rule is (x, y + 2).

Step7: Observe grid transformation

Points move 2 units left and 2 units down, rule is (x - 2, y - 2).

Step8: Observe grid transformation

Points move 4 units right, rule is (x + 4, y).

Step9: Observe grid transformation

x - coordinate decreases by 6 and y - coordinate increases by 6, rule is (x - 6, y + 6).

Step10: Observe grid transformation

It's a rotation, rule is (-y, x).

Step11: Observe grid transformation

Both coordinates are multiplied by 1.5, rule is (1.5x, 1.5y).

Step12: Observe grid transformation

y - coordinate increases by 6, rule is (x, y + 6).

Answer:

1. Translation Left 3 (pink)
2. Rotation 180° CCW (purple)
3. Dilation SF = 4 (orange)
4. (x, -y) (lime green)
5. (-y, x) (purple)
6. (x, y + 2) (purple)
7. (x - 2, y - 2) (yellow)
8. (x + 4, y) (lime green)
9. (x - 6, y + 6) (purple)
10. (-y, x) (pink)
11. (1.5x, 1.5y) (lime green)
12. (x, y + 6) (orange)