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)

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3