Reflected objects are the same distance from but on opposite sides of the line of reflection after the reflection takes place. Translations are done by adding or subtracting values from the x-coordinate if the figure is being moved left or right, and from the y-coordinate if the figure is being moved up or down.
E'(2,- 1), F'(2,- 3), G'(- 2, -3), H'(- 2, - 1)
Practice makes perfect
We want to find the coordinates of the given figure after a reflection and a translation. Let's do it one at time!
Reflection
Let's start by plotting the given points and connecting them to draw our rectangle.
To reflect this figure over the x-axis, we need to plot each vertex of the image E'F'G'H' the same distance from the line of reflection as its corresponding vertex on the preimage EFGH. Because our line of reflection is the x-axis, we will change the sign of the y-coordinates of the points, but the x-coordinates will remain unchanged.
Preimage EFGH
Image E'F'G'H'
Vertex
Distance From the x-axis
Vertex
Distance From the x-axis
E(- 1,1)
1 unit above the x-axis
E'(- 1,- 1)
1 unit below the x-axis
F(-1,3)
3 units above the x-axis
F'(-1,- 3)
3 units below the x-axis
G(- 5,3)
3 units above the x-axis
G'(- 5,- 3)
3 units below the x-axis
H(-5,1)
1 unit above the x-axis
H'(- 5,- 1)
1 unit below the x-axis
Let's do the reflection!
Translation
Now, we will translate the image 3 units to the right.
Translations are done by adding or subtracting values from the x-coordinate if the figure is being moved left or right. Since we want to translate the image 3 units to the right, we will add 3 to the x-coordinate of each vertex.
Vertices of EFGH
(x+3,y)
Vertices of E'F'G'H'
E(- 1,- 1)
(- 1 + 3,- 1)
E'(2,- 1)
F(- 1,- 3)
(- 1 + 3,- 3)
F'(2,- 3)
G(- 5,- 3)
(- 5 + 3,- 3)
G'(- 2,- 3)
H(- 5,- 1)
(- 5 + 3,- 1)
H'(- 2,- 1)
Let's do the translation!
The coordinates of the figure after a reflection and a translation are E'(2,- 1), F'(2,- 3), G'(- 2, -3), and H'(- 2, - 1).
