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skelet666 [1.2K]
3 years ago
12

Suppose triangle ABC has vertices at A(1, 0), B(10, 0), and C(2, 6). After a 60° counterclockwise rotation about the origin, ver

tex B' has coordinates (5, ?).

Mathematics
1 answer:
Artemon [7]3 years ago
3 0
Check the picture attached.

Let OB be the radius of circle with center O.

Let B' be the image of B after the described rotation

OB and OB' are sides of the equilateral triangle OBB'.

The x coordinate of B' is the midpoint of OB, that is 5.

In the right triangle B', point (5, 0) and B:

Distance point (5, 0) to B is 5
|B'B|=|OB|=10

so by the pythagorean theorem:

a= \sqrt{ 10^{2} - 5^{2} } = \sqrt{ 2^{2} *5^{2} - 5^{2} }= \sqrt{5^{2}(4-1)}=5 \sqrt{3} units



Answer: 5 \sqrt{3}

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