Reflected points are the same distance from the line of reflection but on opposite sides of the line before and after the reflection takes place.
A''(10,6), B''(4,6), C''(4,2), D''(10,2)
Practice makes perfect
We are given the vertices of a figure.
A(- 5,3), B(- 2,3), C(- 2,1), D(- 5,1)
Let's start by plotting the vertices in a coordinate plane and connect them with segments to draw our figure.
We want to reflect this figure over the y-axis, then dilate it using a scale factor of 2. Let's do one transformation at time!
Reflection
To reflect the figure, we need to plot each vertex of the image A'B'C'D' the same distance from the line of reflection as its corresponding vertex on the preimage ABCD. Because our line of reflection is the y-axis, this will change the sign of the x-coordinates of the points, but the y-coordinates will remain unchanged.
Preimage ABCD
Image A'B'C'D'
Vertex
Distance From the y-axis
Vertex
Distance From the y-axis
A(- 5,3)
5 units to the left of the y-axis
A'(5,3)
5 units to the right of the y-axis
B(- 2,3)
2 units to the left of the y-axis
B'(2,3)
2 units to the right of the y-axis
C(- 2,1)
2 units to the left of the y-axis
C'(2,1)
2 units to the right of the y-axis
D(- 5,1)
5 units to the left of the y-axis
D'(5,1)
5 units to the right of the y-axis
Let's do the reflection!
Dilation
A dilation can be an enlargement, a reduction, or the same size as the preimage. Which type of dilation it is depends on the value of the scale factor k.
Enlargement
k>1
Reduction
0
Same Size
k=1
When the center of dilation in the coordinate plane is the origin, each coordinate of the preimage is multiplied by the scale factor k to find the coordinates of the image.
ccc
Preimage & & Image [0.5em]
(x,y)& ⇒ & ( kx, ky)
Let's find the coordinates of the vertices of A''B''C''D'' after a dilation with a scale factor k= 2.
Dilation With Scale Factor k=2
Preimage
Multiply by k
Image
A'(5,3)
( 2(5), 2(3))
A''(10,6)
B'(2,3)
( 2(2), 2(3))
B''(4,6)
C'(2,1)
( 2(2), 2(1))
C''(4,2)
D'(5,1)
( 2(5), 2(1))
D''(10,2)
We can now plot the obtained points and connect them with segments to draw the image.
The final vertices of the transformed figure are A''(10,6), B''(4,6), C''(4,2), and D''(10,2).
