Question

x For Exercises 25-28, what is a reflection rule that maps each triangle and its image? SAMPLE 4 25. 03.6), 6-4, -3), 575,) and 0/1, 6). 26. G(9, 12), H(-2. - 15), (3, 8) and G (9,-2), H(-2,25), (3, 2) 27. K(7,-6), L(9. - 3), M(-4, 6) and (7,-4). 219. -7), M(-4, -16)

Answer 1

25. As we see that the y-coordinates does not change, it must be a reflection on a vertical axis. This is a axis of reflection x= constant.

We can use the x-coordinates of the preimage and the image of one point to calculate the axis of reflection, as it has to be in the midpoint:

`\begin{gathered} \text{Axis of reflection}\longrightarrow x=c \\ c=(x^(\prime)+x)/(2)=(1+3)/(2)=(4)/(2)=2_{} \end{gathered}`

The axis of reflection is x=2.

26. In this case, we have an horizontal axis of reflection y=c.

We can find c by calculating the midpoint between the y-coordinates of a point before and after the transformation.

`c=(y^(\prime)+y)/(2)=(-2+12)/(2)=(10)/(2)=5`

The axis of reflection is y=5.

27. Axis of reflection y=-5

`c=(y^(\prime)+y)/(2)=(-4+(-6))/(2)=(-4-6)/(2)=-(10)/(2)=-5`

28. This is a line that acts as axis of reflection.

This line is y=-x.

Then we can write the transformation as:

`(x,y)\longrightarrow(y,-x)`