Core Connections Geometry, 2013
CC
Core Connections Geometry, 2013 View details
Chapter Closure

Exercise 126 Page 270

a Let's first identify the coordinates of the figures vertices.
When performing a rotation of a polygon 180^(∘) clockwise or counterclockwise about the origin, the coordinates of the figures vertices will change in the following way.

preimage (a,b)→ image (- a,- b) Using this rule on the vertices of ABCDE, we can find the vertices of A'B'C'D'E'.

Point (a,b) (- a,- b)
A (- 6,3) (6,- 3)
B (- 4,3) (4,- 3)
C (- 2,5) (2,- 5)
D (- 2,1) (2,- 1)
E (- 6,1) (6,- 1)

When we know the coordinates of the rotated shape, we can draw A'B'C'D'E'.

b When rotating of a polygon 90^(∘) counterclockwise about the origin, the coordinates of the figures vertice's will change in the following way.
preimage (a,b)→ image (- b,a)

Using this rule on the vertices of ABCDE, we can find the vertices of A'B'C'D'E'.

Point (a,b) (- b,a)
A (- 6,3) (- 3,- 6)
B (- 4,3) (- 3,- 4)
C (- 2,5) (- 5,- 2)
D (- 2,1) (-1,- 2)
E (- 6,1) (- 1,- 6)

When we know the coordinates of the rotated shape, we can draw A'B'C'D'E'.

c When performing a reflection of a polygon in the y-axis, the coordinates of the figure's vertices will change in the following way.
preimage (a,b)→ image (- a,b)

Using this rule on the vertices of ABCDE, we can find the vertices of A'B'C'D'E'.

Point (a,b) (- a,b)
A (- 6,3) (6,3)
B (- 4,3) (4,3)
C (- 2,5) (2,5)
D (- 2,1) (2,1)
E (- 6,1) (6,1)

When we know the coordinates of the reflected shape, we can draw A'B'C'D'E'.

d To translate the shape up 5, and left 7, we have to add 5 to the y-coordinate and subtract 7 from the x-coordinate of each vertex.
Point (a,b) (a-7,b+5)
A (- 6,3) (- 13,8)
B (- 4,3) (- 11,10)
C (- 2,5) (- 9,10)
D (- 2,1) (- 9,6)
E (- 6,1) (- 13,5)

When we know the coordinates of the translated shape, we can draw A'B'C'D'E'.