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

Answer:

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

Step-by-step 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 $(2, \, -1)$.

$\begin{array}{cccccc} & \text{Initial} & & \text{After Reflection} & & \text{After translation} \cr A: & (1,\, 1) & \longrightarrow & (1,\, -1) & \longrightarrow & (1,\, 1) \cr B: & (2, \,3) & \longrightarrow & (2,\, -3) & \longrightarrow & (2, \, -1) \cr C: & (3, \,2) & \longrightarrow & (3, \, -2) & \longrightarrow & (3, \, 0) \cr D: & (2, \, 1) & \longrightarrow & (2, \, -1) & \longrightarrow & (2,\, 1) \end{array}$.