GEO.G-GPE.B.4
Use coordinates to prove simple geometric theorems algebraically, including the distance formula and its relationship to the Pythagorean Theorem. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1,√3) lies on the circle centered at the origin and containing the point (0,2).
Example Problems
What is the distance from the following point to the origin?
Round your answer to the nearest hundredth, if necessary.
Round your answer to the nearest hundredth, if necessary.
A circle is centered at and has a radius of .
Where does the point lie: inside the circle, on the circle, or outside the circle?
Where does the point lie: inside the circle, on the circle, or outside the circle?
A circle is centered at and has a radius of .
Where does the point lie: inside the circle, on the circle, or outside the circle?
Where does the point lie: inside the circle, on the circle, or outside the circle?
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