Question

Which algebraic rule describes the 270° counter-clockwise rotation about the origin?

Answer 1

Let's say the point is (x,y) and it lies in 1st quadrant with both x and y as positive ,

Now let's say that the point is rotated by 270 degrees counter clockwise

It means The point will shift to the 4th quadrant , and we know that in 4th quadrant , the x is positive and y is negative ,

Also , as it is rotated by 270 degrees , the x and y values will interchange

SO there are two steps

1) Change the sign of x

2) Interchange the x and y values , i.e swap , x with y and y with x

Answer 2

Rule of rotation describes the {270^ \circ } counter clockwise rotation about the origin.

Further Explanation:

Use the rotation rules to rotate images on the coordinate plane.

The angle in the first quadrant lie between ${0^ \circ }$ to ${90^ \circ }$.

The angle in the second quadrant lie between ${90^ \circ }$ to ${180^ \circ }$.

The angle in the first quadrant lie between ${180^ \circ }$ to ${270^ \circ }$.

The angle in the first quadrant lie between ${270^ \circ }$ to ${360^ \circ }$.

Counter clockwise is the rotation in opposite direction as the hand clock rotates.

Explanation:

Consider a point in the first quadrant.

If we rotate counter clockwise ${90^ \circ }$ the point moves to the second quadrant.

If we rotate counter clockwise ${180^ \circ }$ the point moves to the third quadrant.

If we rotate counter clockwise ${270^ \circ }$ the point moves to the fourth quadrant.

If we rotate counter clockwise ${360^ \circ }$ the point moves to the first quadrant.

In fourth quadrant the $x$-coordinate is positive and the $y$-coordinate is negative.

After rotating ${270^ \circ }$ the value of $x$ and $y$ will interchange.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: translation, equation, $x$- coordinate, $x$- coordinate, first quadrant, second quadrant, third quadrant, fourth quadrant, rotate, ${270^ \circ }$, counter clockwise.