Question

The vertices of polygon ABCD are at A(1, 1), B(2, 3), C(3, 2), and D(2, 1). ABCD is reflected across the x-axis and translated 2 units up to form polygon A′B′C′D′. Match each vertex of polygon A′B′C′D′ to its coordinates.

Answer 1

A' <-----> (1, 1)
B' <-----> (2, -1)
C' <-----> (3, 0)
D' <-----> (2, 1)

Answer 2

• 
  `A^\prime` is at
  `(1, \, 1)`.
• 
  `B^\prime` is at
  `(2, \, -1)`.
• 
  `C^\prime` is at
  `(3,\, 0)`.
• 
  `D^\prime` is at
  `(2, \, 1)`.

Explanation:

To reflect a shape about the
`x`-axis, simply reflect each of its vertex across the
`x`-axis.

The
`y`-coordinate of a point gives the vertical position of the point. On the other hand, the
`x`-axis is horizontal. Reflecting the point would invert the
`y`-coordinate of that point.

For example, reflecting
`B(2,\, 3)` about the
`x`-axis would give
`(2, \, -3)`.

Similarly, to move the polygon up by
`2` units, simply move every one of its vertex up by
`2` 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
`2` units, simply
`2` to its
`y`-coordinate. Aftering moving
`(2, \, -3)`, the reflection of
`B`, up by two units, the new point would have coordinates
`(2, \, -1)`.

`\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}`.