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Coordinate Geometry (angles (a right angle (A Right Triangle (a^2+b^2 =…
Coordinate Geometry
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Proofs
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Steps
- Prove your shape represents the given before you prove the conclusion.
- Label your points and generic coordinates
- Draw a generic shape (think about how you will name it and orient it) TRY TO SITUATE ONE VERTEX ON THE ORIGIN AND ONE SIDE ON AN AXIS
- Show your work to justify your statements (slopes, midpoints, distance, etc.)
- Write as you go (connectors to explain why you are doing what you are doing).
- Make sure to write a conclusion!!!
Lines
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Reletionships
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Perpendicular
The slope of the first lines is equivalent to the opposite reciprocal of the slope to the second line.
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Geometric Figures
Altitude
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You will want to find the perpendicular slope of the line given and the coordinates of the vertex, opposite to the line given. After you have found the slope and point, you can start off your equation with a point-slope form equation.
The altitude is the equation of a line from the opposite vertex to the line given, perpendicular to the slope of the line given.
Median
First you want to find the midpoint of the segment and the coordinates of the vertex opposite to the line. Once you have this, you can find the slope of the line using your two points and then writing an equation with the best point that you think will work out to be easier in the long-run.
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The median is the line from the opposite vertex to the segment given and the midpoint of the given segment.
Perpendicular Bisector
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To find the perpendicular bisector of a segment you use the midpoint formula to find the midpoint of the line, find the slope of the line, then write an equation starting in point-slope form with the midpoint as your point and the perpendicular slop of the slope you found.
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