The rotation of the segment AB is a rigid transformation, the lengths of the preimage and the image remain the same
- The segment hat is the image of AB when rotated 90° counterclockwise around point P is the segment FG
Reason:
Required:
To find the image of the segment AB when rotated 90° counterclockwise
Solution:
The given coordinates of the vertex of the end point of segment AB,
relative to the point P, are;
A(0, 2), B(3, 2)
The coordinates of the image of the point (x, y), following a rotation of 90°
counterclockwise about the origin is (-y, x)
Taking the point P, as the origin, we have;
A(0, 2) → Rot 90°(counterclockwise) → A'(-2, 0)
B(3, 2) → Rot 90°(counterclockwise) → B'(-2, 3)
Which gives;
The coordinates of the image of the segment AB following a rotation of 90°
counterclockwise is the segment A'B' with coordinate A'(-2, 0), and B'(-2, 3),
which is equivalent to the segment FG with coordinates F(-2, 0), and G(-2, 3)
Therefore;
- The segment hat is the image of AB when rotated 90° counterclockwise around point P is the segment FG
Learn more about rotation of a segment here:
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