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°.
