Question

If a segment has endpoints of 0, 4 and 3, 4 how long will a segment be after it's rotated 270° clockwise blank units

Answer 1

To find the length of a segment after it is rotated, we first need to find the distance between the given endpoints. Using the distance formula, we have:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

For the given endpoints, (0, 4) and (3, 4), the distance would be:

Distance = √[(3 - 0)^2 + (4 - 4)^2]
= √[9 + 0]
= √9
= 3 units

Now, to rotate the segment 270° clockwise, we need to identify the new endpoints after the rotation. To do this, we can use rotating transformation rules.

When a point (x, y) is rotated 270° clockwise around the origin, the new coordinates of the point would be (-y, x).

Applying this rule to the first endpoint (0, 4), we have:
(0, 4) → (-4, 0)

Applying the same rule to the second endpoint (3, 4), we have:
(3, 4) → (-4, 3)

Now, we need to find the length of the segment created by these new endpoints. Using the distance formula once again, we have:

Distance = √[(-4 - (-4))^2 + (0 - 3)^2]
= √[0 + 9]
= √9
= 3 units

Therefore, the length of the segment after it is rotated 270° clockwise would still be 3 units.