\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)

Point Reflection

What is a Point Reflection?

Finding Images of Points

Exercise
Find the coordinates of the image of point \(A\) under a point reflection over point \(O\).
\(A'(\)\(,\)\()\)

\(A'(5,2)\)

Exercise
Find the coordinates of the image of point \(B\) under a point reflection over point \(P\).
\(B'(\)\(,\)\()\)

\(B'(6,7)\)

Exercise
Find the coordinates of the image of point \(C\) under a point reflection over point \(Q\).
\(C'(\)\(,\)\()\)

\(C'(1,0)\)

Exercise
Find the coordinates of the image of point \(D\) under a point reflection over point \(R\).
\(D'(\)\(,\)\()\)

\(D'(2,4)\)

Exercise
Find the coordinates of the image of point \(E\) under a point reflection over point \(S\).
\(E'(\)\(,\)\()\)

\(E'(2,7)\)

Exercise
Find the coordinates of the image of point \(F\) under a point reflection over point \(T\).
\(F'(\)\(,\)\()\)

\(F'(1,-2)\)

Finding the Coordinates of the Center of Symmetry

Exercise
The point \(A'\) is the image of point \(A\) under a point reflection over point \(O\).
Find the coordinates of the point \(O\)
\(O(\),\()\)

\(O(3,1)\)

Exercise
The point \(B'\) is the image of point \(B\) under a point reflection over point \(P\).
Find the coordinates of the point \(P\)
\(P(\)\(,\)\()\)

\(P(1,1)\)

Exercise
The point \(C'\) is the image of point \(C\) under a point reflection over point \(Q\).
Find the coordinates of the point \(Q\)
\(Q(\)\(,\)\()\)

\(Q(-1,1)\)

Exercise
The point \(D'\) is the image of point \(D\) under a point reflection over point \(R\).
Find the coordinates of the point \(R\)
\(R(\)\(,\)\()\)

\(R(-1,1)\)

Exercise
The point \(F'\) is the image of point \(F\) under a point reflection over point \(S\).
Find the coordinates of the point \(S\)
\(S(\)\(,\)\()\)

\(S(2,-1)\)

Point Reflections of Figures

Mcq
Is the figure \(\textcolor{colorprop}{A'}\) the image of figure \(\textcolor{colordef}{A}\) under the point reflection over point \(O\)?



Yes

Mcq
Is the figure \(\textcolor{colorprop}{A'}\) the image of figure \(\textcolor{colordef}{A}\) under the point reflection over point \(O\)?



No, the figure \(\textcolor{colorprop}{A'}\) is misplaced. Here is where it should be.

Mcq
Is the figure \(\textcolor{colorprop}{A'}\) the image of figure \(\textcolor{colordef}{A}\) under the point reflection over point \(O\)?



Yes

Mcq
Is the figure \(\textcolor{colorprop}{A'}\) the image of figure \(\textcolor{colordef}{A}\) under the point reflection over point \(O\)?



No, the figure \(\textcolor{colorprop}{A'}\) is misplaced. Here is where it should be.

Drawing Images of Figures

Exercise
Draw the figure \(\textcolor{colorprop}{A'}\), the image of figure \(\textcolor{colordef}{A}\) under the point reflection over point \(O\) (do that on your graph paper).

  1. Draw the image vertices: For each vertex, count the squares to the point \(O\) (left or right, up or down). Place a new point on the other side, the same number of squares away in the opposite direction.
  2. Draw the image figure: Connect the image vertices with lines in the same order as the original figure.

Exercise
Draw the figure \(\textcolor{colorprop}{A'}\), the image of figure \(\textcolor{colordef}{A}\) under the point reflection over point \(O\) (Do that on your graph paper).

  1. Draw the image vertices: For each vertex, count the squares to the point \(O\) (left or right, up or down). Place a new point on the other side, the same number of squares away in the opposite direction.
  2. Draw the image figure: Connect the image vertices with lines in the same order as the original figure.

Exercise
Draw the figure \(\textcolor{colorprop}{A'}\), the image of figure \(\textcolor{colordef}{A}\) under the point reflection over point \(O\) (Do that on your graph paper).

  1. Draw the image vertices: For each vertex, count the squares to the point \(O\) (left or right, up or down). Place a new point on the other side, the same number of squares away in the opposite direction.
  2. Draw the image figure: Connect the image vertices with lines in the same order as the original figure.

Exercise
Draw the figure \(\textcolor{colorprop}{A'}\), the image of figure \(\textcolor{colordef}{A}\) under the point reflection over point \(O\) (Do that on your graph paper).

  1. Draw the image vertices: For each vertex, count the squares to the point \(O\) (left or right, up or down). Place a new point on the other side, the same number of squares away in the opposite direction.
  2. Draw the image figure: Connect the image vertices with lines in the same order as the original figure.

Center of Symmetry

Number of Centers of Symmetry for Common Shapes

Exercise
Count the number of centers of symmetry for the rectangle.
center of symmetry

1 center of symmetry for the rectangle.

Exercise
Count the number of centers of symmetry for the equilateral triangle.
centers of symmetry

0 centers of symmetry for the equilateral triangle.

Exercise
Count the number of centers of symmetry for the square.
center of symmetry

1 center of symmetry for the square.

Exercise
Count the number of centers of symmetry for the parallelogram.
center of symmetry

1 center of symmetry for the parallelogram.

Exercise
Count the number of centers of symmetry for the circle.
center of symmetry

1 center of symmetry for the circle.