Question

Given a point (−7, 4) on a geometric figure, what is the new point after rotating the figure 90 degrees counterclockwise?

-Hiiiiii :)

Answer 1

[AI-generated answer — Bot GPT 3.5]

Hi! To find the new point after rotating the point (-7, 4) 90 degrees counterclockwise, we can use the rotation formula.

The general formula for a counterclockwise rotation of a point (x, y) by an angle θ is:

x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)

In this case, θ = 90 degrees. Let's plug in the values:

x' = (-7)*cos(90) - 4*sin(90)
y' = (-7)*sin(90) + 4*cos(90)

Using the trigonometric values for 90 degrees:

cos(90) = 0
sin(90) = 1

We can simplify the formulas to:

x' = (-7)*0 - 4*1 = -4
y' = (-7)*1 + 4*0 = -7

Therefore, the new point after rotating (-7, 4) 90 degrees counterclockwise is (-4, -7).

Answer 2

Are you sure?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect response earlier. Let's correct it:

To rotate a point (x, y) 90 degrees counterclockwise, we can use the following transformation:

x' = -y
y' = x

Applying this transformation to the given point (-7, 4):

x' = -4
y' = -7

Therefore, the new point after rotating (-7, 4) 90 degrees counterclockwise is (-4, -7).