Rotation 90^(∘) counterclockwise about the origin.
Practice makes perfect
We want to describe the relationship between C(- 7,2) and A(2,7) in terms of rotations. To do so, let's start by plotting these two points on a coordinate plane.
A rotation, or turn, is a transformation in which a figure is rotated about a point called the center of rotation. The number of degrees a figure rotates is the angle of rotation. Let's rotate A counterclockwise about the origin to visualize this relationship.
It appears as though C(- 7,2) is the image of A(2,7) after a rotation of 90^(∘) counterclockwise about the origin.
Checking Our Answer
We can confirm this mathematically by using the rules for rotations in the coordinate plane.
Rotations in the Coordinate Plane
When a point (x,y) is rotated counterclockwise about the origin, the following relations are true.
90^(∘)Rotation: & (x,y)→ (- y,x)
180^(∘)Rotation: & (x,y)→ (- x,- y)
270^(∘)Rotation: & (x,y)→ (y,- x)
Comparing the points to the rules, we can see that this transformation is indeed a 90^(∘) rotation counterclockwise about the origin.
ccc
( x, y) & → & (- y, x) [0.5em]
A( 2, 7) & & C(- 7, 2)
