Question

What is the angle of rotation from figure D to figure D’? Assume that the center of rotation is the origin.

Answer 1

Explanation:

It's 90 degrees clockwise.

Answer 2

Angle of rotation is 90°.

Explanation:

In the given figure point D is rotated about the origin and we get a new point D'

We join D and D' with origin by two lines forming oD and oD'

Now we get slopes of oD as
`m_(1)` and oD' as
`m_(2)`

Point D and D'are (-1.5, 3.5) and (3.5, 1.5) and origin as (0,0)

`m_(1)` =
`((3.5-0))/((-1.5-0))=(-3.5)/(7.5)`

= -
`(7)/(3)`

`m_(2)` =
`((1.5-0))/((3.5-0))=(1.5)/(7.5)`

=
`(3)/(7)`

Now
`m_(1)` ×
`m_(2)` =
`((-7)/(3))((3)/(7))`

= -
`((7*3)/(3*7))=(-1)`

Therefore, both the lines oD and oD' are perpendicular to each other.

Angle of rotation is 90°.