Question

practice performing a reflection in the coordinate plane
study the example showing a reflection across the y - axis. then solve problems 1 - 5.
example
tessa used reflections to design a pattern. she draws figure ghij in the coordinate plane. how might she have reflected figure ghij across the y - axis to form figure ghij?
tessa could have counted the number of units from each vertex to the y - axis. then she could have counted the same number of units on the other side of the y - axis to plot the corresponding vertices of figure ghij.

1. tessa can now use her graph in the example to find the coordinates of the vertices of figure ghij. how could she have found these coordinates without drawing the reflection of figure ghij?
2. isabel draws figure ghij in the coordinate plane. he wants to reflect figure ghij across the x - axis to form figure wxyz.

a. draw a dashed line to show the line of reflection.
b. draw figure wxyz.

Explanation:

Step1: Recall reflection rule

For a reflection across the y - axis, the rule for a point $(x,y)$ is $(x,y)\to(-x,y)$. So, if we know the coordinates of the vertices of figure GHIJ as $(x_1,y_1),(x_2,y_2),\cdots$, the coordinates of the vertices of its reflection G'H'I'J' across the y - axis are $(-x_1,y_1),(-x_2,y_2),\cdots$.

Step2: For reflection across x - axis

The rule for reflecting a point $(x,y)$ across the x - axis is $(x,y)\to(x, - y)$.

a.

To show the line of reflection across the x - axis, draw a horizontal dashed line along the x - axis (the line $y = 0$).

b.

To draw figure WXYZ, take each vertex $(x,y)$ of figure GHIJ and find its image $(x,-y)$ using the reflection - across - x - axis rule and then connect the new vertices to form figure WXYZ.

Answer:

For the first part (finding coordinates without drawing reflection across y - axis): Use the rule $(x,y)\to(-x,y)$ for each vertex of figure GHIJ.
For part a: Draw a horizontal dashed line along the x - axis ($y = 0$).
For part b: Use the rule $(x,y)\to(x,-y)$ for each vertex of figure GHIJ to find the vertices of WXYZ and then draw figure WXYZ.