Question

URGENT: Figure C and figure E shown on the coordinate plane blow a transformation was performed on figure C to create figure D. Then, a transformation was performed on figure D to create figure E

As a result of the series of transformation performed, figure C is similar figure E, however these figures are not congruent

1• justify why figures C And E are similar and not congruent

2• describe a transformation applied to figure C that will create figure D and then a transformation performed on figure D that will create Figure E

Answer 1

1. Whereby one square = One unit, we have;

Lengths of the sides of figure C are;

4, √(4² + 2²), √(4² + 2²) which simplifies to 4, 2·√5, 2·√5

Lengths of the sides of figure E are;

2, √(1² + 2²), √(1² + 2²) which simplifies to 2, √5, √5

Figure E is equivalent to figure C scaled down by a factor of 1/2

The trigonometric ratios of the two figures are therefore equal and figure C is similar to figure E but figure C is larger than figure E

2. A transformation that will create figure D from figure C is a rotation, 90° counter clockwise about the point (2, -2)

A transformation that will create figure E from figure D is a dilation of figure D by 1/2 with the midpoint of figure D being the center of dilation

Explanation: