Rectangle PQRS is rotated 90° clockwise about the origin. On a coordinate plane, rectangle P Q R S has points (negative 3, negative 1), (negative 1, negative 1), (negative 1, negative 4), (negative 3, negative 4). What are the coordinates of R'?

Therefore the new coordinate of R is (4,3).

Step-by-step explanation:

Rectangle:

If the origin rotates 90° clockwise. After the rotation of origin let the new coordinate of (x,y) will be (x',y')

Then the relation between them is

x=x'cos(-90°)-y sin(-90°)  

⇒x=(x'×0)+y'(-1)                 [ sin(-90°)= -1  and cos(- 90°)= 0]

⇒ x= -y'(1)

and y= x'sin(90°)+y'cos(-90°)

⇒y=x'(-1)+(y'×0)

⇒y= -x'(2)

The original coordinate of R is (-3,-4).

Here x= -3  and y = -4

putting the value of x and y in equation (1) and (2)

- 3= -y'

⇒y'=3

And -4= -x'

⇒x'=4

Therefore the new coordinate of R is (4,3).

R'(-4,1)

Step-by-step explanation:

The vertices of rectangle PQRS are P(-3,-1), Q(-1,-1), R(-1,-4) and S(-3,-4).

It is given that Rectangle PQRS is rotated 90° clockwise about the origin.

We need to find the coordinates of R'.

The rule of rotation is

Using this rule, the coordinates of R' are

Therefore, the coordinates of R' are (-4,1).

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