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)

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

898.1666667

step-by-step explanation:

5389/6 = 898.1666667