Question

Please help this is very important

1. Rotate JKQ 180 degrees about the origin

2. Rotate BSL 90 degrees counterclockwise about the origin

3. Rotate UHF 90 degrees clockwise about the origin

4. Rotate JVYR 180 degrees about the origin


(Attachment is below)

Answer 1

Here's what I get.

Explanation:

1. Rotate 180° about origin

The formula for rotation of a point (x,y) by an angle θ about the origin is

x' = xcosθ - ysinθ

y' = ycosθ + xsinθ

If θ = 180°, sinθ = 0 and cosθ = -1, and the formula becomes

x' = -x

y' = -y

The rule is then (x, y) ⟶ (-x, -y).

H: (-3, -5) ⟶ (3, 5)

J: (-5, -3) ⟶ (5, 3)

Q: (0, -1) ⟶ (0, 1)

The vertices of H'J'Q' are (3, 5), (5, 3), and (0, 1).

2. Rotation 90° counterclockwise about origin

cos90° = 0 and sin90° = 1

x' = xcos90° - ysin90° = -y

y' = ycos90° + xsin90° = x

The rule is then (x, y) ⟶ (-y, x).

B: (4, 5) ⟶ (-5, 4)

L: (5, 0) ⟶ (0, 5)

S: (2, 2) ⟶ (-2, 2)

The vertices of B'L'S' are (-5, 4), (0, 5), and (-2, 2).

3. Rotation 90° clockwise about origin

cos(-90°) = 0 and sin(-90°) = -1

x' = xcos(-90°) - ysin(-90°) = y

y' = ycos(-90°) + xsin(-90°) = -x

The rule is then (x, y) ⟶ (y, -x).

F: (1, -5) ⟶ (-5, -1)

H: (-2, -3) ⟶ (-3, 2)

U: (-4, -5) ⟶ (-5, 4)

The vertices of F'H'U' are (-5, -1), (-3, -2), and (-5, 4).

4. Rotate 180° about origin

The rule is (x, y) ⟶ (-x, -y).

J: (1, -1) ⟶ (-1, 1)

V: (2, 0) ⟶ (-2, 0)

Y: (5, -3) ⟶ (-5, 3)

R: (4, -3) ⟶ (-4, 3)

The vertices of J'V'Y'R' are (-1, 1), (-2, 0), (-5, 3), and (-4, 3).

The figures below show your shapes before and after the rotations.