Answer:
Option (1)
1) Segment B'D' will run through (2, 2) and will be shorter than segment BD.
Explanation:
The rest of the question is the attached figure (1).
The statement options are:
1) Segment B'D' will run through (2, 2) and will be shorter than segment BD.
2) Segment B'D' will run through (2, 2) and will be longer than segment BD.
3) Segment B'D' will parallel to segment BD and will be shorter than segment BD.
4) Segment B'D' will be parallel to segment BD and will be longer than segment BD.
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See the attched figure (2), which represents Quadrilateral ABCD and the image A'B'C'D'
As shown:
The quadrilateral ABCD with vertices A(1,2), B(2,3), C(4,2) and D(2,1).
Quadrilateral ABCD is dilated by a scale factor of 1 over 2 centered around (2, 2).
So,
The quadrilateral A'B'C'D' will be with vertices:
A'= (1.5,2), B'= (2,2.5), C'= (3,2), D'= (2,1.5)
Comparing the options with the figure (2):
So, the answer is option (1)
1) Segment B'D' will run through (2, 2) and will be shorter than segment BD.