Question

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'?

Answer 1

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

Explanation:

Rectangle:

• The number of vertices of a rectangle is 4 and the number of edges of a rectangle is 4.

• The diagonals bisect each other at 90°.
• The sum of all four angles are 360°.

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).

Answer 2

R'(-4,1)

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

`(x,y)\rightarrow (y,-x)`

Using this rule, the coordinates of R' are

`R(-1,-4)\rightarrow R'(-4,-(-1))`

`R(-1,-4)\rightarrow R'(-4,1)`

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