reflections across the x- or y- axis practice

Answer 1

Sure! Here are some practice problems involving reflections across the x-axis and y-axis. I'll provide both the problems and the solutions.

Practice Problems

1. Point Reflection

   • Reflect the point \( A(3, 5) \) across the x-axis.
   • Reflect the point \( B(-2, 4) \) across the y-axis.

2. Find the Image Points

   • The point \( C(1, -3) \) is reflected across the y-axis. What are the coordinates of the reflected point?
   • The point \( D(-4, 2) \) is reflected across the x-axis. What are the coordinates of the reflected point?

3. Graphing Reflections

   • Plot the points \( E(2, 3) \) and \( F(-1, -4) \). Then reflect them across the x-axis and y-axis, respectively, and plot the new points.

4. Distance Between Points

   • If point \( G(4, 6) \) is reflected across the x-axis and then point \( H(4, -6) \) is created. What is the distance between point \( G \) and point \( H \)?

Solutions

1. Point Reflection

   • Reflection of \( A(3, 5) \) across the x-axis:
     The new point \( A' \) will be \( (3, -5) \).
   • Reflection of \( B(-2, 4) \) across the y-axis:
     The new point \( B' \) will be \( (2, 4) \).

2. Find the Image Points

   • Reflection of \( C(1, -3) \) across the y-axis:
     The new point \( C' \) will be \( (-1, -3) \).
   • Reflection of \( D(-4, 2) \) across the x-axis:
     The new point \( D' \) will be \( (-4, -2) \).

3. Graphing Reflections

   • Original points to plot:
     • \( E(2, 3) \) reflects to \( (2, -3) \) across x-axis.
     • \( F(-1, -4) \) reflects to \( (1, -4) \) across y-axis.
   • After plotting, you will have four points on the graph:
     • \( E(2, 3) \), \( E'(2, -3) \), \( F(-1, -4) \), and \( F'(1, -4) \).

4. Distance Between Points

   • The distance between \( G(4, 6) \) and \( H(4, -6) \) can be calculated using the distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \): \[ d = \sqrt{(4 - 4)^2 + (-6 - 6)^2} = \sqrt{0 + (-12)^2} = \sqrt{144} = 12. \]

Feel free to ask if you would like more practice problems or explanations!