Consider the individual options.
M)
A figure in quadrant II is reflected into quadrant III.
We know that the point in quadrant II is (-x,y) and the point in quadrant III is (-x,-y).
Recall that the reflection of point (x, y) across the x-axis is (x, -y).
![(-x,y)\rightarrow *(-x,-y)](https://img.qammunity.org/2023/formulas/mathematics/college/v8f5ew8snffp610wd8hf6sbgd72bej11ha.png)
A figure in quadrant II is reflected into quadrant III is reflected over the x-axis.
N)
![(12,-7)\rightarrow(-12,-7)](https://img.qammunity.org/2023/formulas/mathematics/college/1rn63ltm3jd56v6dhovfmnbt7pppy17j5r.png)
Let x=12 and y =-7 and substitute in the given, we get
![(x,y)\rightarrow(-x,y)](https://img.qammunity.org/2023/formulas/mathematics/college/ikcitr9ov18gnuy0131ezdtc936qt485rg.png)
Recall that the reflection of point (x, y) across the y-axis is (-x, y).
Answer:
![(12,-7)\rightarrow(-12,-7)\text{ is reflected over the y-axis.}](https://img.qammunity.org/2023/formulas/mathematics/college/kc371ogchb7y6xnc63certx6hr6uacnxg4.png)
O)
The point H(-1,4) is reflected to H' (1,4).
![(-1,4)\rightarrow(1,4)](https://img.qammunity.org/2023/formulas/mathematics/college/x9n85ehcy1vrod1djnpsssmutp3alb60kj.png)
Let x=-1 and y =4 and substitute in the given, we get
![(x,y)\rightarrow(-x,y)](https://img.qammunity.org/2023/formulas/mathematics/college/ikcitr9ov18gnuy0131ezdtc936qt485rg.png)
Recall that the reflection of point (x, y) across the y-axis is (-x, y).
The point H(-1,4) is reflected to H' (1,4) is reflected over the y-axis.
P)
The axis line between two stars is the x-axis.
The given image is reflected over the x=axis.
Q)
The point R(-3,7) is reflected into quadrant III.
The point on quadrant III is of the form (-x,-y).
Let x =-3 and y =7 and the given can be written as follows.
![(x,y)\rightarrow(x,-y)](https://img.qammunity.org/2023/formulas/mathematics/college/d7a29ae1nc5itoub5zbvfqbwxpczq9rzr6.png)
Recall that the reflection of point (x, y) across the x-axis is (x, -y).
The point R(-3,7) is reflected into quadrant III is reflected over the x-axis.
R)
![(a,b)\rightarrow(a,-b)](https://img.qammunity.org/2023/formulas/mathematics/college/lscvrlqooh4aontaeaypge0a0uwsfzxr5o.png)
Recall that the reflection of point (x, y) across the x-axis is (x, -y).
Answer:
![(a,b)\rightarrow(a,-b)\text{ is reflected over the x-axis.}](https://img.qammunity.org/2023/formulas/mathematics/college/tgetbrnboh01s3pl6wu49ny7x4j5axgqet.png)
S)
Point B(-10,-7) is reflected into quadrant IV.
The point on quadrant III is of the form (x,-y).
Let x =-10 and y =-7 and the given can be written as follows.
![(x,y)\rightarrow(-x,y)](https://img.qammunity.org/2023/formulas/mathematics/college/ikcitr9ov18gnuy0131ezdtc936qt485rg.png)
Recall that the reflection of point (x, y) across the y-axis is (-x, y).
Point B(-10,-7) is reflected into quadrant IV is reflected over the y-axis.
T)
![(c,d)\rightarrow(-c,d)](https://img.qammunity.org/2023/formulas/mathematics/college/v8rz2sa7v53kp74aiqvg4ih1siyfrwtt7w.png)
Recall that the reflection of point (x, y) across the y-axis is (-x, y).
Answer:
![(c,d)\rightarrow(-c,d)\text{ is reflected over the y-axis.}](https://img.qammunity.org/2023/formulas/mathematics/college/jtj6tcgronvvvxak0xubnf4gokp7rcr8z5.png)