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LekaFEV [45]
2 years ago
13

Quadrilateral A’B’C’D’ is a dilation of quadrilateral ABCD about point P. Quadrilateral ABCD is shown. Side AB is labeled 5. Sid

e BC is labeled 4. Side CD is labeled 10. Side DA is labeled 6. Quadrilateral A prime B prime C prime D prime is between quadrilateral ABCD and point P. Side A prime B prime is labeled 1 and one fourth. Side B prime C prime is labeled one. Side C prime D prime is labeled 2 and a half. Side D prime A prime is labeled 1 and a half. reduction enlargement

Mathematics
2 answers:
Stolb23 [73]2 years ago
5 0

Answer:  The correct option is (A) reduction.

Step-by-step explanation:  Given that the quadrilateral A'B'C'D' is a dilation of the quadrilateral ABCD.

As shown in the given figure, the lengths of the sides of quadrilateral ABCD are as follows:

AB = 5 units, BC = 4 units, CD = 10 units and DA = 6 units.

And, the lengths of the sides of quadrilateral A'B'C'D' are as follows:

A'B'=1\dfrac{1}{4}=\dfrac{5}{4}~\textup{units},~~B'C'=1~\textup{units},~~C'D'=2\dfrac{1}{2}=\dfrac{5}{2}~\textup{units},\\\\D'A'=1\dfrac{1}{2}=\dfrac{3}{2}~\textup{units}.

We know that the dilation will be an enlargement if the scale factor is greater than 1 and it will be a reduction if the scale factor is less than 1.

Now, the scale factor is given by

S=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}\\\\\\\Rightarrow S=\dfrac{A'B'}{AB}=\dfrac{\frac{5}{4}}{5}=\dfrac{5}{4\times5}=\dfrac{1}{4}

Since the scale factor is less than 1, so the dilation will be a reduction.

navik [9.2K]2 years ago
5 0

Answer:

A reduction

Step-by-step explanation:

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