Question

The image of the point (4,-2) under a rotation 180 degrees about the origin is:

Answer 1

(-4, 2) is the answer.

Explanation:

Given the point (4,-2).

To find:

Image of point under a rotation of
`180^\circ` about the origin.

Solution:

First of all, let us learn about the quadrant system.

There are four quadrants in the xy-coordinate system.

Each quadrant is at
`90^\circ` with each other that means, if we rotate any point by
`90^\circ`, one quadrant gets changed.

If we rotate by another
`90^\circ`, one more quadrant will get changed.

OR

we can say that if the rotation is performed by
`180^\circ` about the original, the point will go to its diagonally opposite quadrant.

1. A point in 1st quadrant, rotated by
`180^\circ`, about origin will go to 3rd quadrant.

2. A point in 2nd quadrant, rotated by
`180^\circ`, about origin will go to 4th quadrant.

3. A point in 3rd quadrant, rotated by
`180^\circ`, about origin will go to 1st quadrant.

4. A point in 4th quadrant, rotated by
`180^\circ`, about origin will go to 1st quadrant.

Here, the given point is in 4th quadrant. so it will go to 2nd quadrant.

And hence, both the signs will change.

x coordinate will be -4 and

y coordinate will be 2.

Please refer to the image attached as well.

The angle of rotation is
`180^\circ`.

Resultant point will be (-4, 2).