Question

Quadrilateral ABCD is dilated by a scale factor of 1 over 3 centered around (1, 2). Which statement is true about the dilation?

Answer 1

Note: Since you missed to add the figure. So, after a little research I am kind of able to find the figure and hence, assuming it as a reference. Hence, I am attaching the figure and solution of that figure is also visible in the same figure. Please check the attached figure (a)

Answer:

Segment B'D' will be parallel to segment BD and will be shorter than segment BD. Please see the attached figure (a) for better understanding.

Step-by-step explanation:

As we know that there are certain rules when a quadrilateral is dilated by a certain scale centered around a certain point.

So,

Let suppose P(a, b) is the point.

The dilation rule by a scale factor of 1 over 3 or (1/3) centered around (1, 2) is

P(a, b) → $P(\frac{x+2}{3}, \frac{y+4}{3})$

Hence,

            A(1, 2) → A'(1, 2)

            B(2, 3) → B'(4/3, 7/3)

            C(4, 2) → C'(2, 2)

             D(2, 1) → D'(4/3, 5/3)

The attached figure show that if we draw the all these points in the coordinate plan i.e. A(1, 2), B(2, 3), C(4, 2), D(2, 1) and A'(1, 2), B'(4/3, 7/3), C'(2, 2), D'(4/3, 5/3), we can determine that Segment B'D' will be parallel to segment BD and will be shorter than segment BD.

Keywords: dilation, quadrilateral, segment

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