Question

The vertices of a figure are P(-3, 4), Q(-1, 4), R(-2, 1), and S(-4,1). Rotate the figure 270° clockwise about the

origin. What will the coordinates be after your rotate them

Answer 1

After a 270° clockwise rotation about the origin, the vertices of the figure with original coordinates P(-3, 4), Q(-1, 4), R(-2, 1), and S(-4,1) become P'(4, 3), Q'(4, 1), R'(1, 2), and S'(1, 4).

To rotate a point (x, y) counterclockwise about the origin by θ, the new coordinates (x', y') can be found using the formulas:

`\[ x' = x \cos(\theta) - y \sin(\theta) \]\[ y' = x \sin(\theta) + y \cos(\theta) \]`

For a 270° clockwise rotation, the formulas become:

`\[ x' = x \cos(270^\circ) - y \sin(270^\circ) \]\[ y' = x \sin(270^\circ) + y \cos(270^\circ) \]`

Simplify using trigonometric values:

x' = -y

y' = x

Now, apply these formulas to each vertex of the figure:

1. For P(-3, 4): P' = (4, 3)

2. For Q(-1, 4): Q' = (4, 1)

3. For R(-2, 1): R' = (1, 2)

4. For S(-4, 1): S' = (1, 4)

After a 270° clockwise rotation, the new coordinates are: P'(4, 3), Q'(4, 1), R'(1, 2), S'(1, 4)