Question

1. identify transformation rule

9a. which rule reflects over the x - axis?
a. (x,y)→(x, - y)
b. (x,y)→( - x,y)
c. (x,y)→( - x, - y)
d. (x,y)→(y,x)
9b. which rule shifts 2 units down?
a. (x,y)→(x,y - 2)
b. (x,y)→(x - 2,y)
c. (x,y)→(x + 2,y + 2)
d. (x,y)→( - x, - y)
9c. which rule reflects across the y - axis?
a. (x,y)→(x, - y)
b. (x,y)→( - x,y)
c. (x,y)→( - x, - y)
d. (x,y)→(y, - x)
9d. which rule translates 3 left and 4 up?
a. (x,y)→(x - 3,y + 4)
b. (x,y)→(x + 3,y - 4)
c. (x,y)→(x + 4,y - 3)
d. (x,y)→(x - 4,y + 3)

Explanation:

Step1: Recall x - axis reflection rule

When reflecting a point $(x,y)$ over the x - axis, the x - coordinate remains the same and the y - coordinate changes sign. So the rule is $(x,y)\to(x, - y)$.

Step2: Recall y - axis reflection rule

When reflecting a point $(x,y)$ over the y - axis, the y - coordinate remains the same and the x - coordinate changes sign. So the rule is $(x,y)\to(-x,y)$.

Step3: Recall vertical shift rule

A vertical shift of $k$ units down for a point $(x,y)$ changes the y - coordinate. The rule is $(x,y)\to(x,y - k)$. For a shift of 2 units down, $k = 2$ and the rule is $(x,y)\to(x,y - 2)$.

Step4: Recall horizontal and vertical translation rule

A translation of $a$ units left and $b$ units up for a point $(x,y)$ gives the rule $(x,y)\to(x - a,y + b)$. For a translation of 3 units left and 4 units up, $a = 3$ and $b = 4$, so the rule is $(x,y)\to(x - 3,y+4)$.

Answer:

9a. A. $(x,y)\to(x, - y)$
9b. B. $(x,y)\to(x,y - 2)$
9c. C. $(x,y)\to(-x,y)$
9d. A. $(x,y)\to(x - 3,y + 4)$