Question

1. if a point in quadrant ii is reflected in the x - axis, its image will be in quadrant

a. i b. ii c. iii d. iv

1. reflecting (5,1) in the y - axis yields an image of

a. (5, - 1) b. (-5, - 1)
c. (5,1) d. (-5,1)

1. using the translation that maps (3, - 4) to its image (1,0), what is the image of any point (x,y)?

a. (x + 2,y + 4) b. (x - 2,y - 4)
c. (x + 2,y - 4) d. (x - 2,y + 4)

Explanation:

Step1: Understand reflection in x - axis

When a point $(x,y)$ is reflected in the $x$ - axis, the rule is $(x,y)\to(x, - y)$. A point in Quadrant II has coordinates $(-x,y)$ where $x>0$ and $y > 0$. After reflection in the $x$ - axis, the new point is $(-x,-y)$ which lies in Quadrant III.

Step2: Understand reflection in y - axis

When a point $(x,y)$ is reflected in the $y$ - axis, the rule is $(x,y)\to(-x,y)$. For the point $(5,1)$, its reflection in the $y$ - axis is $(-5,1)$.

Step3: Find the translation rule

The translation that maps $(3,-4)$ to $(1,0)$: Let the translation be $(x,y)\to(x + a,y + b)$. Then $3 + a=1$ and $-4 + b = 0$. Solving $3 + a=1$ gives $a=1 - 3=-2$, and solving $-4 + b = 0$ gives $b = 4$. So the translation rule for any point $(x,y)$ is $(x,y)\to(x-2,y + 4)$.

Answer:

1. C. III
2. D. $(-5,1)$
3. D. $(x - 2,y + 4)$