We are told that GHJK has vertices at G(-3,- 1), H(-3,2), J(4, 2), and K(4,-1). Let's draw it on the coordinate plane.
We will sketch the image of the above rectangle after a reflection across the x-axis, followed by a dilation by a scale factor of 2. Let's do these transformations one at a time.
Reflection
We will start by reflecting GHJK across the x-axis. To do so, we will consider the x-axis as the line of symmetry.
We see that the image of GHJK after a reflection across the x-axis has vertices G'(-3,1), H'(- 3,-2), J'(4,-2), and K'(4,1).
Dilation
Finally, we will dilate â–³G'H'J'K' by a scale factor of 2. Be aware that if the center of dilation is not specified, we consider the origin O(0,0) as the center of dilation. To obtain the images of the vertices, we multiply their coordinates by the scale factor 2.
G'H'J'K'
G''H''J''K''
G'(- 3,1)
G''(- 3* 2, 1* 2) ⇒ G''(- 6,2)
H'(- 3,-2)
H''(- 3* 2, -2* 2) ⇒ H''(- 6,-4)
J'(4,-2)
J''(4* 2, -2* 2) ⇒ J''(8,-4)
K'(4,1)
K''(4* 2, 1* 2) ⇒ K''(8,2)
Let's now show the image of G'H'J'K' after a dilation by a scale factor of 2, G''H''J''K''.
