Question

The point (-3,-2) is rotated 180 degrees about the origin. what are the coordinates of its image?

Answer 1

The coordinates of the image are (3 , 2)

Explanation:

* Lets explain how to solve the problem

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 180° anti-clock wise

∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° anti-clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180° clock wise

∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° clock wise

∴ Its image is (-y , x)

* There is no difference between rotating 180° clockwise or

anti-clockwise around the origin

* Lets solve the problem

∵ The point (-3 , -2) is rotated 180° about the orange

∵ The image of the point (x , y) when rotated about the origin by

angle 180° is (-x , -y)

∵ x = -3 , then -x = -(-3) = 3

∵ y = -2 , then -y = -(-2) = 2

∴ The coordinates of the image are (3 , 2)

Answer 2

The coordinates of the image are (3,2)

Explanation:

we know that

The coordinates of the pre-image are (-3,-2)

This point is located on III Quadrant

If the point is rotated 180 degrees about the origin

then

The image will be located on I Quadrant

The rule of the rotation is equal to

(x,y) ------> (-x,-y)

so

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