Answer:
(-4, 2) is the answer.
Step-by-step explanation:
Given the point (4,-2).
To find:
Image of point under a rotation of [tex]180^\circ[/tex] 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 [tex]90^\circ[/tex] with each other that means, if we rotate any point by [tex]90^\circ[/tex], one quadrant gets changed.
If we rotate by another [tex]90^\circ[/tex], one more quadrant will get changed.
OR
we can say that if the rotation is performed by [tex]180^\circ[/tex] about the original, the point will go to its diagonally opposite quadrant.
1. A point in 1st quadrant, rotated by [tex]180^\circ[/tex], about origin will go to 3rd quadrant.
2. A point in 2nd quadrant, rotated by [tex]180^\circ[/tex], about origin will go to 4th quadrant.
3. A point in 3rd quadrant, rotated by [tex]180^\circ[/tex], about origin will go to 1st quadrant.
4. A point in 4th quadrant, rotated by [tex]180^\circ[/tex], 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 [tex]180^\circ[/tex].
Resultant point will be (-4, 2).
