The point (5, -2) is rotated 90° about the origin. Its image is
To rotate a point 90° about the origin, we need to find the new coordinates after the rotation.
To do this, we can use the following formulas for a 90° counterclockwise rotation about the origin:
New x-coordinate = -y-coordinate
New y-coordinate = x-coordinate
Given the point (5, -2), let's calculate its image after the rotation:
New x-coordinate = -(-2) = 2
New y-coordinate = 5
Therefore, the image of the point (5, -2) after a 90° rotation about the origin is (2, 5).
To find the image of the point (5, -2) after rotating it 90° about the origin, we can use the following steps:
Step 1: Draw a coordinate plane, representing the x-y plane.
Step 2: Plot the point (5, -2) on the coordinate plane. This point is located 5 units to the right and 2 units below the origin.
Step 3: To rotate the point 90° about the origin, we can use the rotation matrix:
[ cos(θ) -sin(θ) ]
[ sin(θ) cos(θ) ]
Since we want to rotate the point 90° counterclockwise, the angle θ would be π/2 radians.
Step 4: Multiply the coordinates of the point (5, -2) by the rotation matrix:
[ cos(π/2) -sin(π/2) ] [ 5 ]
[ sin(π/2) cos(π/2) ] * [-2 ]
Simplifying this, we get:
[ 0 -1 ] [ 5 ]
[ 1 0 ] * [-2 ]
Step 5: Perform the matrix multiplication:
[ 0*(-2) + (-1)*5 ]
[ 1*(-2) + 0*5 ]
Simplifying further, we get:
[ -5 ]
[ -2 ]
Therefore, after rotating the point (5, -2) 90° counterclockwise about the origin, its image is (-5, -2).