Answer :
Answer:
- [tex]A^\prime[/tex] is at [tex](1, \, 1)[/tex].
- [tex]B^\prime[/tex] is at [tex](2, \, -1)[/tex].
- [tex]C^\prime[/tex] is at [tex](3,\, 0)[/tex].
- [tex]D^\prime[/tex] is at [tex](2, \, 1)[/tex].
Step-by-step explanation:
To reflect a shape about the [tex]x[/tex]-axis, simply reflect each of its vertex across the [tex]x[/tex]-axis.
The [tex]y[/tex]-coordinate of a point gives the vertical position of the point. On the other hand, the [tex]x[/tex]-axis is horizontal. Reflecting the point would invert the [tex]y[/tex]-coordinate of that point.
For example, reflecting [tex]B(2,\, 3)[/tex] about the [tex]x[/tex]-axis would give [tex](2, \, -3)[/tex].
Similarly, to move the polygon up by [tex]2[/tex] units, simply move every one of its vertex up by [tex]2[/tex] units. Keep in mind that the order of the translation does matter. In this question, reflect each point before moving them upward.
To move a point up by [tex]2[/tex] units, simply [tex]2[/tex] to its [tex]y[/tex]-coordinate. Aftering moving [tex](2, \, -3)[/tex], the reflection of [tex]B[/tex], up by two units, the new point would have coordinates [tex](2, \, -1)[/tex].
[tex]\begin{array}{cccccc} & \text{Initial} & & \text{After Reflection} & & \text{After translation} \cr A: & (1,\, 1) & \longrightarrow & (1,\, -1) & \longrightarrow & (1,\, 1) \cr B: & (2, \,3) & \longrightarrow & (2,\, -3) & \longrightarrow & (2, \, -1) \cr C: & (3, \,2) & \longrightarrow & (3, \, -2) & \longrightarrow & (3, \, 0) \cr D: & (2, \, 1) & \longrightarrow & (2, \, -1) & \longrightarrow & (2,\, 1) \end{array}[/tex].
Answer:
A' <-----> (1, 1)
B' <-----> (2, -1)
C' <-----> (3, 0)
D' <-----> (2, 1)