What is the result of rotating the triangle 90° counterclockwise around the point (2, -1)?
the first one is the one that is rotated

(0, 2) -> (-1, -3)

(1, 5) -> (-4, -2)

(3, 1) -> (0, 0)

Step-by-step explanation:

The general rule for a rotation 90° counterclockwise around the origin if you have a point (x, y) -> (-y, x). But since this isnt around the origin. You need to do a simple step before applying the rule.

To each point you want to rotate you need to substract the point that is the center of the rotation.

The points of the triangle are:

(0, 2)

(1, 5)

(3, 1)

Now you have to substract (2, -1) to each of them

(0, 2) - (2, -1) = (-2, 3)

(1, 5) - (2, -1) = (-1, 6)

(3, 1) - (2, -1) = (1, 2)

And with the new points you apply the rule for rotation (x,y) -> (-y,x)

(-2, 3) -> (-3, -2)

(-1, 6) -> (-6, -1)

(1, 2) -> (-2, 1)

And now you add the previously substracted point (center of rotation).

(-3, -2) + (2, -1) = (-1, -3)

(-6, -1) + (2, -1) = (-4, -2)

(-2, 1) + (2, -1 = (0, 0)

this doesn't make sense lol

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²