What do you recall about transformations in a plane? what is important to remember about transformations? what's the difference between rigid transformations and nonrigid transformations?

1)

Any image in a plane could be altered by using different operations, or transformations. Here are the most common types:

2)

Transformations map one set of points onto another set of points, generally with the purpose of changing the position, size, and/or shape of the figure made up by the first set of points. The first set of points, from the domain of the transformation, is called the set of pre-images, whereas the second set of points, from the range of the transformation, is called the set of images. Therefore, a transformation maps each pre-image point to its image point.

3)

Reflections, translations, rotations, and combinations of these three transformations are "rigid transformations".

      example is dilation.  

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft