graph the triangle 90° clockwise about the origin A= (4,-3) B= (4,0) C= (8,0)

Answer 1

To graph the triangle 90° clockwise about the origin, we need to rotate each point 90° clockwise.

We can find the coordinates of the new points using the rotation matrix:

[x', y'] = [xcosθ - ysinθ, xsinθ + ycosθ]

where θ is the angle of rotation (90° in this case).

For point A (4, -3):
[x', y'] = [4cos90 - (-3)sin90, 4sin90 + (-3)cos90]
= [4(0) - (-3)(1), 4(1) + (-3)(0)]
= [3, 4]

So, the new coordinates for point A are (3, 4).

For point B (4, 0):
[x', y'] = [4cos90 - 0sin90, 4sin90 + 0cos90]
= [4(0) - 0(1), 4(1) + 0(0)]
= [0, 4]

So, the new coordinates for point B are (0, 4).

For point C (8, 0):
[x', y'] = [8cos90 - 0sin90, 8sin90 + 0cos90]
= [8(0) - 0(1), 8(1) + 0(0)]
= [0, 8]

So, the new coordinates for point C are (0, 8).

Therefore, the triangle after rotating 90° clockwise about the origin is:
A'(3, 4), B'(0, 4), C'(0, 8).

To graph this triangle, you can plot the points A'(3, 4), B'(0, 4), and C'(0, 8) on a coordinate grid.