What is the new point after rotating the point (3, -5) 180° clockwise?
11 answers
The new point after rotating the point (3, -5) 180° clockwise would be (-3, 5).
If a segment has endpoints (0, 4) and (3, 4), how long will the segment be after it is rotated 270° clockwise?
To find the length of the segment after it is rotated 270° clockwise, we need to find the new coordinates of the endpoints and then calculate the distance between them.
To rotate a point (x, y) 270° clockwise about the origin, we can use the formula:
new_x = -y
new_y = x
Applying this formula to the endpoints of the segment:
new_x1 = -4
new_y1 = 0
new_x2 = -4
new_y2 = 3
The new endpoints after rotation are (-4, 0) and (-4, 3).
To calculate the length of the segment, we can use the distance formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Calculating the length of the segment:
distance = √((-4 - (-4))^2 + (3 - 0)^2)
= √(0^2 + 3^2)
= √(0 + 9)
= √9
= 3
Therefore, the segment will be 3 units long after it is rotated 270° clockwise.
To rotate a point (x, y) 270° clockwise about the origin, we can use the formula:
new_x = -y
new_y = x
Applying this formula to the endpoints of the segment:
new_x1 = -4
new_y1 = 0
new_x2 = -4
new_y2 = 3
The new endpoints after rotation are (-4, 0) and (-4, 3).
To calculate the length of the segment, we can use the distance formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Calculating the length of the segment:
distance = √((-4 - (-4))^2 + (3 - 0)^2)
= √(0^2 + 3^2)
= √(0 + 9)
= √9
= 3
Therefore, the segment will be 3 units long after it is rotated 270° clockwise.
A square with sides 6 units in length is reflected across the x-axis. how long are the sides in the reflected figure?
When a square is reflected across the x-axis, each side of the square remains the same length. Therefore, the sides of the reflected figure will also be 6 units in length.
A triangle with an area of 25 square units is rotated 180° clockwise. what is the area of the rotated figure?
When a figure is rotated by 180°, its area remains the same. Therefore, the area of the rotated figure will also be 25 square units.
Demonstrating the properties of rotations, if a line segment with endpoints (0, -3) and (0, -7) is rotated 90° clockwise, what is an endpoint of this rotated segment?
To rotate a point (x, y) 90° clockwise about the origin, we can use the following formulas:
new_x = y
new_y = -x
Applying these formulas to the endpoints of the line segment:
For the first endpoint (0, -3):
new_x1 = -3
new_y1 = 0
For the second endpoint (0, -7):
new_x2 = -7
new_y2 = 0
Therefore, the endpoints of the rotated segment are (-3, 0) and (-7, 0).
new_x = y
new_y = -x
Applying these formulas to the endpoints of the line segment:
For the first endpoint (0, -3):
new_x1 = -3
new_y1 = 0
For the second endpoint (0, -7):
new_x2 = -7
new_y2 = 0
Therefore, the endpoints of the rotated segment are (-3, 0) and (-7, 0).
Rotate a point on a line at (-4, 6) 180° counterclockwise. What is the resulting point?
To rotate a point (x, y) 180° counterclockwise about the origin, we can use the following formulas:
new_x = -x
new_y = -y
Applying these formulas to the point (-4, 6):
new_x = -(-4) = 4
new_y = -(6) = -6
Therefore, the resulting point after rotating (-4, 6) 180° counterclockwise is (4, -6).
new_x = -x
new_y = -y
Applying these formulas to the point (-4, 6):
new_x = -(-4) = 4
new_y = -(6) = -6
Therefore, the resulting point after rotating (-4, 6) 180° counterclockwise is (4, -6).
1 answer