Question

2. Describe a rigid motion or composition of rigid motions that maps the rectangular bench at (0, 10)and

the adjacent flagpole onto the other short rectangular bench and flagpole.

Answer 1

See Explanation

Explanation:

Given

Let the bench be B and the flagpole be T.

So:

`B = (0,10)` --- given

The flagpole is represented by the triangular shape labelled T.

So, we have:

`T = (6,9)`

See attachment for the rectangular bench and the flagpole

From the attached image, the location of the other bench is:

`B' = (0,-10)`

And the location of the other flagpole is:

`T' = (-6,9)`

So, we have:

`B = (0,10)` ==>
`B' = (0,-10)`

`T = (6,9)` ==>
`T' = (-6,9)`

When a point is reflected from
`(x,y)` to
`(x,-y)`, the transformation rule is reflection across x-axis.

So the rigid transformation that takes
`B = (0,10)` to
`B' = (0,-10)` is: reflection across x-axis.

When a point is reflected from
`(x,y)` to
`(-x,y)`, the transformation rule is reflection across y-axis.

So the rigid transformation that takes
`T = (6,9)` to
`T' = (-6,9)` is: reflection across y-axis.