"Point B (4,0) is rotated 45 degrees clockwise about the origin. Write the exact coordinates of B'."
B' is ... (2√2 , -2√2)
Make a sketch of the right-angled triangle with angle 45° and hypotenuse of 4
sin45 = y/4, cos45 = x/4
y = 4(√2/2) , x = 4√2/2
new point = B(2√2 , -2√2)
Thanks so much!
To find the coordinates of B' after rotating a point clockwise about the origin, you can use the following steps:
1. Identify the coordinates of the original point B.
Given: B(4, 0)
2. Apply the rotation formula.
In a clockwise rotation about the origin, the new coordinates (B') can be determined using the following formulas:
x' = x * cos(angle) + y * sin(angle)
y' = -x * sin(angle) + y * cos(angle)
3. Substitute the values into the formulas.
Using the rotation angle of 45 degrees (π/4 in radians), we can substitute the values for B into the formulas:
x' = 4 * cos(π/4) + 0 * sin(π/4)
y' = -4 * sin(π/4) + 0 * cos(π/4)
4. Evaluate the trigonometric functions.
Simplify the trigonometric functions using their respective values:
x' = 4 * (√2/2) + 0
y' = -4 * (√2/2) + 0
5. Calculate the coordinates of B'.
Evaluate the equations to find the new coordinates of B':
x' = 4 * (√2/2) + 0 = 4√2/2 = 2√2
y' = -4 * (√2/2) + 0 = -4√2/2 = -2√2
Therefore, the exact coordinates of B' after rotating B(4,0) 45 degrees clockwise about the origin are B'(2√2, -2√2).