Question

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

Answer 1

Answer:

Step-by-step explanation:

It's 90 degrees clockwise.

Answer 2

Answer:

Angle of rotation is 90°.

Step-by-step 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)

$m_{1}$ = $\frac{(3.5-0)}{(-1.5-0)}=\frac{-3.5}{7.5}$

= -$\frac{7}{3}$

$m_{2}$ = $\frac{(1.5-0)}{(3.5-0)}=\frac{1.5}{7.5}$

= $\frac{3}{7}$

Now $m_{1}$ × $m_{2}$ = $(\frac{-7}{3})(\frac{3}{7})$

= - $(\frac{7*3}{3*7})=(-1)$

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

Angle of rotation is 90°.