The blue preimage is 2 times larger than the green image.
Example Solution: A reflection in the y-axis followed by a dilation with a scale factor of 12.
Practice makes perfect
To find a similarity transformation that maps the blue preimage to the green preimage, let's start with their orientation.
Notice that all the corresponding vertices, except the ones on the y-axis, are pointing in the opposite directions. Therefore, if we reflect quadrilateral JKLM in the y-axis, figures will have the same orientation. Recall that, according to the coordinates rule, two points reflected in the y-axis have opposite x-coordinates.
(a,b)
(- a, b)
J(6,2)
J'(-6,2)
K(6,6)
K'(-6,6)
L(-2,8)
L'(2,8)
M(0,2)
M'(0,2)
Now we can graph the image of quadrilateral JKLM after a reflection in the y -axis.
We can see that the figures have the same orientation. However, they differ in size, so we need to perform a dilation. But what scale factor should we choose? If we compare two corresponding sides, such as J'K' and PQ, we notice that J'K' is twice as long as PQ.
Therefore, if we dilate quadrilateral J'K'L'M' with a scale factor of 12, figures will have the same size. According to the coordinate rule, we need to multiply all the coordinates by 12.
(a,b)
(1/2a,1/2b)
J'(- 6,2)
J''(- 3,1)
K'(-6,6)
K''(-3,3)
L'(2,8)
L''(1,4)
M'(0,2)
M''(0,1)
Once we know the coordinates, let's plot them.
We can see that the figures mapped onto each other. Therefore, the similarity transformation that maps quadrilateral JKLM to quadrilateral PQRS is a reflection in the y-axis followed by a dilation with a scale factor of 12.
