Which polygons can be mapped onto each other by similarity transformations?
Graph shows 4 polygons plotted on a coordinate plane. Polygon 1 at A(0.5, 0.5), B(0.5, 4.5), C(2.5, 6.5), D(3.5, 4.5), E(3.5, 0.5). Polygon 2 at F(4, 0.5), G(4, 2.5), H(6, 2.5), I(7, 1), J(6, 0.5). Polygon 3 at K(4, 3), L(4, 5), M(7, 5), N(8, 4.5).
To determine which polygons can be mapped onto each other by similarity transformations, we need to compare their corresponding angles and side lengths.
If two polygons have the same corresponding angles and proportional side lengths, then they can be mapped onto each other by a similarity transformation.
Looking at the given polygons:
Polygon 1: A(0.5, 0.5), B(0.5, 4.5), C(2.5, 6.5), D(3.5, 4.5), E(3.5, 0.5)
Polygon 2: F(4, 0.5), G(4, 2.5), H(6, 2.5), I(7, 1), J(6, 0.5)
Polygon 3: K(4, 3), L(4, 5), M(7, 5), N(8, 4.5)
Comparing Polygon 1 and Polygon 2, we can see that their corresponding angles are different and their side lengths are also not proportional. Therefore, Polygon 1 and Polygon 2 cannot be mapped onto each other by similarity transformations.
Similarly, comparing Polygon 1 and Polygon 3, we can see that their corresponding angles are different and their side lengths are also not proportional. Therefore, Polygon 1 and Polygon 3 cannot be mapped onto each other by similarity transformations.
However, there is not enough information provided to determine whether Polygon 2 and Polygon 3 can be mapped onto each other by similarity transformations.