All side lengths in quadrilateral PQRS measure 4 units. A transformation maps PQRS to P'Q'R'S'. All sides of P'Q'R'S' measure 1

Question

2 years ago

13

All side lengths in quadrilateral PQRS measure 4 units. A transformation maps PQRS to P'Q'R'S'. All sides of P'Q'R'S' measure 1

unit. Is the transformation an isometric transformation? Explain. Yes, the side lengths in the two figures are proportional. Yes, one figure maps to the other. No, the side lengths are not preserved. No, the angles are not preserved.

Mathematics

2 answers:

VladimirAG [237] · Answer 1 · 2022-05-25T05:03:02+03:00

VladimirAG [237]2 years ago

6 0

The answer is no, the side lengths are not persevered. <span />

Dmitry [639] · Answer 2 · 2022-05-25T07:14:18+03:00

Answer:

No, the side lengths are not preserved.

Step by step explanation:

We have been given that all side lengths in quadrilateral PQRS measure 4 units. A transformation maps PQRS to P'Q'R'S'. All sides of P'Q'R'S' measure 1 unit.

We can see that the transformation that maps PQRS to P'Q'R'S' is dilation as after dilating our pre-image PQRS with a factor of $\frac{1}{4}$ we get our image P'Q'R'S'.

Since we know that isometry does not change the shape or size of the figure and isometric figures are said to be geometrically congruent. In our case our side lengths are shrunken so the given transformation is not isometric.

Therefore, our transformation is not isometric as the side lengths are not preserved.