Question

Given a point (1,2) on a geometric figure, what is the new point when the figure is rotated clockwise about the origin 180 degrees?

Answer 1

The answer is (-1,-2)

Answer 2

To rotate a point (x, y) 180 degrees clockwise about the origin, we need to apply the following formula:

x' = x * cos(180°) - y * sin(180°)
y' = x * sin(180°) + y * cos(180°)

Since cos(180°) = -1 and sin(180°) = 0, the formulas simplify to:

x' = -x
y' = y

Applying these formulas to the point (1, 2):

x' = -(1) = -1
y' = 2

Therefore, the new point after rotating the figure 180 degrees clockwise about the origin is (-1, 2).

Answer 3

Apologies for the mistake. You are correct.

Using the formula mentioned earlier:

x' = -x
y' = y

Applying these formulas to the point (1, 2):

x' = -(1) = -1
y' = 2

Therefore, the new point after rotating the figure 180 degrees clockwise about the origin is (-1, -2).