Graph the triangle ABC after a 90 clockwise rotation around the center at origin
a 4, -3
b 4, 0
c 9, 0
To graph the triangle ABC after a 90-degree clockwise rotation around the origin, we need to apply the following transformation to each vertex:
(x', y') = (xcos(theta) + ysin(theta), -xsin(theta) + ycos(theta))
For a 90-degree clockwise rotation, theta = -90 degrees or -pi/2 radians.
Let's apply this transformation to each vertex:
Vertex A'(x', y') = (4*cos(-pi/2) + (-3)*sin(-pi/2), -4*sin(-pi/2) + (-3)*cos(-pi/2))
= (4*0 + (-3)*(-1), -4*(-1) + (-3)*0)
= (3, -4)
Vertex B'(x', y') = (4*cos(-pi/2) + 0*sin(-pi/2), -4*sin(-pi/2) + 0*cos(-pi/2))
= (4*0 + 0*1, -4*(-1) + 0*0)
= (0, 4)
Vertex C'(x', y') = (9*cos(-pi/2) + 0*sin(-pi/2), -9*sin(-pi/2) + 0*cos(-pi/2))
= (9*0 + 0*1, -9*(-1) + 0*0)
= (0, 9)
The new coordinates for each vertex are:
A' (3, -4)
B' (0, 4)
C' (0, 9)
Now we can graph the triangle ABC and its rotated image:
Triangle ABC:
Vertex A (4, -3)
Vertex B (4, 0)
Vertex C (9, 0)
Triangle A'B'C':
Vertex A' (3, -4)
Vertex B' (0, 4)
Vertex C' (0, 9)
Plot these points on a coordinate plane and connect them to form the triangles ABC and A'B'C'.