Respuesta :
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
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 [tex]{0^ \circ }[/tex] to [tex]{90^ \circ }[/tex].
The angle in the second quadrant lie between [tex]{90^ \circ }[/tex] to [tex]{180^ \circ }[/tex].
The angle in the first quadrant lie between [tex]{180^ \circ }[/tex] to [tex]{270^ \circ }[/tex].
The angle in the first quadrant lie between [tex]{270^ \circ }[/tex] to [tex]{360^ \circ }[/tex].
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 [tex]{90^ \circ }[/tex] the point moves to the second quadrant.
If we rotate counter clockwise [tex]{180^ \circ }[/tex] the point moves to the third quadrant.
If we rotate counter clockwise [tex]{270^ \circ }[/tex] the point moves to the fourth quadrant.
If we rotate counter clockwise [tex]{360^ \circ }[/tex] the point moves to the first quadrant.
In fourth quadrant the [tex]x[/tex]-coordinate is positive and the [tex]y[/tex]-coordinate is negative.
After rotating [tex]{270^ \circ }[/tex] the value of [tex]x[/tex] and [tex]y[/tex] will interchange.
Learn more:
1. Learn more about inverse of the function https://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 https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: translation, equation, [tex]x[/tex]- coordinate, [tex]x[/tex]- coordinate, first quadrant, second quadrant, third quadrant, fourth quadrant, rotate, [tex]{270^ \circ }[/tex], counter clockwise.
