demostrating the properties or rotations, if a line segment with endpoints (0, -3) and (0, -7) is rotated 90 degrees clockwise, what is an endpoint of this rotated segment?
To demonstrate the rotation, let's first find the midpoint of the line segment. The midpoint can be found by taking the average of the x-coordinates and the average of the y-coordinates.
x-coordinate of the midpoint = (0 + 0)/2 = 0/2 = 0
y-coordinate of the midpoint = (-3 + -7)/2 = -10/2 = -5
So, the midpoint of the line segment is (0, -5).
Now, let's perform a 90-degree clockwise rotation around the midpoint.
To rotate a point (x, y) 90 degrees clockwise, the new coordinates are found by using the following formulas:
x' = x*cos(90°) + y*sin(90°)
y' = -x*sin(90°) + y*cos(90°)
Substituting the coordinates of the midpoint into these formulas, we get:
x' = 0*cos(90°) + (-5)*sin(90°) = 0 + (-5) = -5
y' = -0*sin(90°) + (-5)*cos(90°) = -0 + 0 = 0
So, the endpoint of the rotated segment is (-5, 0).
demostrating the properties or rotations, if a line segment with endpoints (0, -3) and (0, -7) is rotated 90 degrees clockwise, what is an endpoint of this rotated segment?
a. (3, 0)
b. (0, 7)
c. (0, 7)
b. (-3, 0)
To rotate a point (x, y) 90 degrees clockwise, we can use the following rotation formulas:
x' = y
y' = -x
Let's apply these formulas to the endpoints of the line segment.
For the endpoint (0, -3):
x' = (-3)
y' = -0
So, the rotated coordinates of this endpoint are (-3, 0).
For the endpoint (0, -7):
x' = (-7)
y' = -0
So, the rotated coordinates of this endpoint are (-7, 0).
Thus, the correct answer is option b) (-7, 0).
demostrating the properties or rotations, if a line segment with endpoints (0, -3) and (0, -7) is rotated 90 degrees clockwise, what is an endpoint of this rotated segment?
a. (3, 0)
b. (0, 3)
c. (0, 7)
d. (-3, 0)
Apologies for the oversight in my previous response.
To perform a 90-degree clockwise rotation, we can use the following rotation formulas:
x' = y
y' = -x
Let's apply these formulas to the endpoints of the line segment.
For the first endpoint (0, -3):
x' = (-3)
y' = 0
So, the rotated coordinates of this endpoint are (-3, 0).
For the second endpoint (0, -7):
x' = (-7)
y' = 0
So, the rotated coordinates of this endpoint are (-7, 0).
Thus, the correct answer is option d) (-3, 0).