Question

8. Rectangle ABCD has vertices A (-1, 2), B (4, 22. C(4, -1), and D(-1,-1).Rectangle ABCD is dilated using the algebraic representation (x, y)*( x, y).(8.30)A. Rectangle ABCD and rectangle A'B'C'D' are congruent.B. Rectangle ABCD and rectangle A'B'C'D' are similar. Rectangle ABCD islarger than rectangle A'B'C'D.C. Rectangle ABCD and rectangle A'B'C'D' are similar. Rectangle ABCD issmaller than rectangle A'B'CD'.D. Rectangle ABCD and rectangle A'B'C'D' are similar. Rectangle ABCD isthe same size as rectangle A'B'C'D'.

Answer 1

The given transformation is

`(x,y)\rightarrow((3)/(4)x,(3)/(4)y)`

The given points are-

`A(-1,2),B(4,22),C(4,-1),D(-1,-1)`

Now, we apply the dilation to each point. We just have to multiply each coordinate with the scale factor 3/4.

`A^(\prime)(-1\cdot(3)/(4),2\cdot(3)/(4))\rightarrow A^(\prime)(-(3)/(4),(3)/(2))`
`B^(\prime)(4\cdot(3)/(4),22\cdot(3)/(4))\rightarrow B^(\prime)(3,(33)/(2))`
`C^(\prime)(4\cdot(3)/(4),-1\cdot(3)/(4))\rightarrow C^(\prime)(3,-(3)/(4))`
`D^(\prime)(-1\cdot(3)/(4),-1\cdot(3)/(4))\rightarrow D^(\prime)(-(3)/(4),-(3)/(4))`

As you can observe, the new coordinates are less than the originals, this means the image is smaller than the pre-image.

Therefore, the right answer is B.