Line segment AB is shown on a coordinate grid:
The line segment is rotated 270 degrees counterclockwise about the origin to form A'B'. Which statement describes A'B'?
1. A'B' is parallel to AB.
2. A'B' is half the length of AB.
3. A'B' and AB are equal in length.
4. A'B' is greater than twice the length of AB
Answers
Line segment AB is shown on a coordinate grid:
The line segment is rotated 270 degrees counterclockwise about the origin to form A'B'.
A'B' and AB are equal in length.
Given : Line segment AB
The line segment is rotated 270 degrees counterclockwise about the origin to form A'B'.
To Find : Which statement describes A'B'?
1. A'B' is parallel to AB.
2. A'B' is half the length of AB.
3. A'B' and AB are equal in length.
4. A'B' is greater than twice the length of AB.
Solution:
Line segment AB
The line segment is rotated 270 degrees counterclockwise
Rotations in form of (2n-1)*90° will make line perpendicular
Hence 3 x 90° = 270° A'B' will be perpendicular to AB
Rotation in multiple of 180°
180n will make line parallel
Rotation does not change size but only position
Hence A'B' is half the length of AB. is not possible
A'B' is greater than twice the length of AB. is not possible
A'B' and AB are equal in length is correct option
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