Question

coordinate plane study the example showing a reflection across the y-axis. then solve problems 1–5. example tessa uses 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 jabari 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:

Problem 1

To find the coordinates of the reflected figure \( G'H'I'J' \) across the \( y \)-axis without drawing, Tessa can use the rule for reflecting a point \( (x,y) \) across the \( y \)-axis, which is \( (x,y)\to(-x,y) \). She would take the coordinates of each vertex of \( GHIJ \), change the sign of the \( x \)-coordinate (keep the \( y \)-coordinate the same), and those would be the coordinates of the corresponding vertices of \( G'H'I'J' \).

The line of reflection for a reflection across the \( x \)-axis is the \( x \)-axis itself (the line \( y = 0 \)). To show it, draw a dashed horizontal line along the \( x \)-axis (where \( y = 0 \)) on the coordinate plane provided for Jabari's figure.

To reflect figure \( GHIJ \) across the \( x \)-axis to form \( WXYZ \), use the reflection rule over the \( x \)-axis: for a point \( (x,y) \), the reflected point is \( (x, -y) \). First, identify the coordinates of vertices \( G \), \( H \), \( I \), \( J \) from the graph. Then, for each vertex, keep the \( x \)-coordinate the same and change the sign of the \( y \)-coordinate. Plot these new points and connect them to form \( WXYZ \). For example, if \( G \) has coordinates \( (1, 5) \) (estimating from the grid), its reflection \( W \) would be \( (1, -5) \); similarly for other vertices.

Answer:

Tessa can use the reflection rule over the \( y \)-axis: for a point \((x, y)\) on \( GHIJ \), the reflected point on \( G'H'I'J' \) is \((-x, y)\). She finds the \( x \)- and \( y \)-coordinates of each vertex of \( GHIJ \), applies \( (x,y)\to(-x,y) \) to each, and uses those new coordinates for \( G'H'I'J' \).

Problem 2a