Question

your turn

1. match the quote to the correct coordinate

rules for reflection on a coordinate
plane
d. reflection across the x - axis
$(x,y)\to(x, - y)$
quote
a. “to reflect the figure, all x values will take the
opposite sign; all y values will remain the same.”
b. “to reflect the figure, all x values will be the
opposite sign of the y values; all y values will be
the opposite sign of the x values.”
c. “to reflect the figure, all x values will be the y
values; all y values will be the x values.”
d. “to reflect the figure, all x values will remain the
same; all y values will take the opposite sign.”
reflection across the y - axis
$(x,y)\to( - x,y)$
reflection across line $y = x$
$(x,y)\to(y,x)$
reflection across line $y = - x$
$(x,y)\to( - y, - x)$

Explanation:

Step1: Recall reflection rules

• Reflection across the \(x -\)axis:
• The rule for reflecting a point \((x,y)\) across the \(x -\)axis is \((x,y)\to(x, - y)\). When we reflect a point across the \(x -\)axis, the \(x -\)coordinate remains the same, and the \(y -\)coordinate changes its sign. So, for all points in the figure, the \(x -\)values remain the same, and the \(y -\)values take the opposite sign. This matches quote A: “To reflect the figure, all \(x\) values will take the same sign; all \(y\) values will remain the same”.
• Reflection across the \(y -\)axis:
• The rule for reflecting a point \((x,y)\) across the \(y -\)axis is \((x,y)\to(-x,y)\). When we reflect a point across the \(y -\)axis, the \(y -\)coordinate remains the same, and the \(x -\)coordinate changes its sign. So, for all points in the figure, the \(y -\)values remain the same, and the \(x -\)values take the opposite sign. This matches quote B: “To reflect the figure, all \(x\) values will be the opposite sign of the \(y\) values; all \(y\) values will be the same”.
• Reflection across the line \(y = x\):
• The rule for reflecting a point \((x,y)\) across the line \(y=x\) is \((x,y)\to(y,x)\). When we reflect a point across the line \(y = x\), the \(x\) and \(y\) coordinates are swapped. So, for all points in the figure, the \(x\) and \(y\) values are swapped. This matches quote C: “To reflect the figure, all \(x\) values will be the \(y\) values; all \(y\) values will be the \(x\) values”.
• Reflection across the line \(y=-x\):
• The rule for reflecting a point \((x,y)\) across the line \(y =-x\) is \((x,y)\to(-y,-x)\). When we reflect a point across the line \(y=-x\), the \(x\) and \(y\) coordinates are swapped and their signs are changed. So, for all points in the figure, the \(x\) values take the opposite sign of the original \(y\) values and the \(y\) values take the opposite sign of the original \(x\) values. This matches quote D: “To reflect the figure, all \(x\) values will remain the same; all \(y\) values will take the opposite sign”.

Answer:

• Reflection across the \(x -\)axis: A. “To reflect the figure, all \(x\) values will take the same sign; all \(y\) values will remain the same”
• Reflection across the \(y -\)axis: B. “To reflect the figure, all \(x\) values will be the opposite sign of the \(y\) values; all \(y\) values will be the same”
• Reflection across the line \(y = x\): C. “To reflect the figure, all \(x\) values will be the \(y\) values; all \(y\) values will be the \(x\) values”
• Reflection across the line \(y=-x\): D. “To reflect the figure, all \(x\) values will remain the same; all \(y\) values will take the opposite sign”