Question

1. describe a translation

10a. which describes (x,y)→(x + 5,y - 2)?
a. 5 right, 2 down
b. 5 left, 2 up
c. 2 right, 5 up
d. 2 left, 5 down
10b. which describes (x,y)→(x - 3,y + 4)?
a. 3 left, 4 up
b. 3 right, 4 down
c. 4 left, 3 up
d. 4 right, 3 down
10c. which describes (x,y)→(x - 7,y - 1)?
a. 7 right, 1 up
b. 7 left, 1 down
c. 1 left, 7 down
d. 7 down, 1 left
10d. which describes (x,y)→(x + 6,y + 2)?
a. 6 left, 2 down
b. 6 right, 2 up
c. 2 left, 6 up
d. 2 right, 6 down

1. reflection over axes

11a. which reflection produces (x,y)→(-x,y)?
a. y - axis
b. x - axis
c. origin
d. line y = x
11b. which reflection produces (x,y)→(x,-y)?
a. y - axis
b. x - axis
c. origin
d. line y=-x

Explanation:

Step1: Recall translation rules

For a translation $(x,y)\to(x + a,y + b)$, $a$ is horizontal shift and $b$ is vertical shift. Positive $a$ is right - shift, negative $a$ is left - shift. Positive $b$ is up - shift, negative $b$ is down - shift.

Step2: Analyze 10a

For $(x,y)\to(x + 5,y-2)$, $a = 5$ (5 units right) and $b=-2$ (2 units down). So the answer is A. 5 right, 2 down.

Step3: Analyze 10b

For $(x,y)\to(x - 3,y + 4)$, $a=-3$ (3 units left) and $b = 4$ (4 units up). So the answer is C. 3 left, 4 up.

Step4: Analyze 10c

For $(x,y)\to(x - 7,y - 1)$, $a=-7$ (7 units left) and $b=-1$ (1 unit down). So the answer is B. 7 left, 1 down.

Step5: Analyze 10d

For $(x,y)\to(x + 6,y + 2)$, $a = 6$ (6 units right) and $b = 2$ (2 units up). So the answer is B. 6 right, 2 up.

Step6: Recall reflection rules

Reflection of $(x,y)$ over the y - axis gives $(-x,y)$. Reflection of $(x,y)$ over the x - axis gives $(x,-y)$.

Step7: Analyze 11a

Since reflection of $(x,y)$ over the y - axis gives $(-x,y)$, the answer is A. y - axis.

Step8: Analyze 11b

Since reflection of $(x,y)$ over the x - axis gives $(x,-y)$, the answer is B. x - axis.

Answer:

10a. A. 5 right, 2 down
10b. C. 3 left, 4 up
10c. B. 7 left, 1 down
10d. B. 6 right, 2 up
11a. A. y - axis
11b. B. x - axis