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?

Answer 1

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).

Answer 2

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)

Answer 3

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).

Answer 4

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)

Answer 5

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).