Question

Give the coordinates of M, N, O, P', and Q, after rotating figure MNOPQ 270° counterclockwise about the origin.

A) M: (4, -4), N: (-2, -4), O: (-2, 0), P': (-4, 2), Q: (2, 2)
B) M: (4, -4), N: (-4, -2), O: (0, -2), P': (2, -4), Q: (2, 4)
C) M: (4, -4), N: (-4, -2), O: (-2, 0), P': (-4, -4), Q: (2, 2)
D) M: (-4, 4), N: (-4, -2), O: (-2, 0), P': (2, -4), Q: (4, 2)

Answer 1

To rotate a figure counterclockwise 270° about the origin, we can use the rotation formulas. Plugging in the coordinates of each point, we get the new coordinates for M, N, O, P', and Q.

Step-by-step explanation:

To rotate a point counterclockwise about the origin, we can use the rotation formulas:

x' = x cos(q) + y sin(q)

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

Plugging in the coordinates of each point:

M: (4, -4)

x' = 4 cos(270°) + (-4) sin(270°) = 4(0) + (-4)(-1) = 4

y' = -4 sin(270°) + (-4) cos(270°) = (-4)(-1) + (-4)(0) = 4

So, M: (4, 4)

Using the same process:

N: (-2, -4)

x' = -2 cos(270°) + (-4) sin(270°) = -2(0) + (-4)(-1) = -4

y' = -4 sin(270°) + (-4) cos(270°) = (-4)(-1) + (-4)(0) = 4

So, N: (-4, 4)

O: (-2, 0)

x' = -2 cos(270°) + 0 sin(270°) = -2(0) + 0 = 0

y' = 0 sin(270°) + 0 cos(270°) = 0(0) + 0(0) = 0

So, O: (0, 0)

P': (-4, 2)

x' = -4 cos(270°) + 2 sin(270°) = -4(0) + 2(-1) = -2

y' = 2 sin(270°) + 2 cos(270°) = 2(-1) + 2(0) = -2

So, P': (-2, -2)

Q: (2, 2)

x' = 2 cos(270°) + 2 sin(270°) = 2(0) + 2(-1) = -2

y' = 2 sin(270°) + 2 cos(270°) = 2(-1) + 2(0) = -2

So, Q: (-2, -2)