What are the coordinate points of A′ if A (5, 6) undergoes a rotation of:

Question

90° clockwise:

270° clockwise:

Answer 1

To find the coordinate points of A' after a rotation of 90° clockwise and 270° clockwise, we can use the rotation matrix formula:

For a rotation of 90° clockwise:

x' = x cos(theta) - y sin(theta)
y' = x sin(theta) + y cos(theta)

Using A(5, 6), we have:
x = 5
y = 6
theta = 90°

Plugging these values into the rotation matrix formula:

x' = 5 cos(90°) - 6 sin(90°)
= 5 (0) - 6 (1)
= -6

y' = 5 sin(90°) + 6 cos(90°)
= 5 (1) + 6 (0)
= 5

Therefore, the coordinate points of A' after a rotation of 90° clockwise is A'(-6, 5).

For a rotation of 270° clockwise:

x' = x cos(theta) - y sin(theta)
y' = x sin(theta) + y cos(theta)

Using A(5, 6), we have:
x = 5
y = 6
theta = 270°

Plugging these values into the rotation matrix formula:

x' = 5 cos(270°) - 6 sin(270°)
= 5 (0) - 6 (-1)
= 6

y' = 5 sin(270°) + 6 cos(270°)
= 5 (-1) + 6 (0)
= -5

Therefore, the coordinate points of A' after a rotation of 270° clockwise is A'(6, -5).

Answer 2

What are the coordinate points of A′ if A (5, 6) undergoes a rotation of:
180° clockwise:

180° counterclockwise:

Answer 3

To find the coordinate points of A' after a rotation of 180° clockwise and 180° counterclockwise, we again use the rotation matrix formula.

For a rotation of 180° clockwise:

x' = x cos(theta) - y sin(theta)
y' = x sin(theta) + y cos(theta)

Using A(5, 6), we have:
x = 5
y = 6
theta = 180°

Plugging these values into the rotation matrix formula:

x' = 5 cos(180°) - 6 sin(180°)
= 5 (-1) - 6 (0)
= -5

y' = 5 sin(180°) + 6 cos(180°)
= 5 (0) + 6 (-1)
= -6

Therefore, the coordinate points of A' after a rotation of 180° clockwise is A'(-5, -6).

For a rotation of 180° counterclockwise, we can simply take the negative of the coordinate points after a 180° clockwise rotation. Therefore, the coordinate points of A' after a rotation of 180° counterclockwise are A'(5, 6).

Answer 4

180° counterclockwise:

Answer 5

To find the coordinate points of A' after a rotation of 180° counterclockwise, we use the same rotation matrix formula:

x' = x cos(theta) - y sin(theta)
y' = x sin(theta) + y cos(theta)

Using A(5, 6), we have:
x = 5
y = 6
theta = 180°

Plugging these values into the rotation matrix formula:

x' = 5 cos(180°) - 6 sin(180°)
= 5 (-1) - 6 (0)
= -5

y' = 5 sin(180°) + 6 cos(180°)
= 5 (0) + 6 (1)
= 6

Therefore, the coordinate points of A' after a rotation of 180° counterclockwise is A'(-5, 6).