Trivium
- Given an origin point and two perpendicular coordinate axes in a plane, use a ruler to determine the rectangular coordinates of any point in that plane.
- Given the rectangular coordinates of two points in space, calculate the distance between them and their midpoint.
- Given the rectangular coordinates of two points in space, determine an equation of the line that contains those points.
- Given two non-parallel lines in space, determine the coordinates of the point at which they intersect.
- Given a point in space and a slope, know the equation of the line with that slope that passes through that point, and vice versa: given an equation corresponding to a line, recognize it as the equation of a line, and determine its slope.
- Given a point in space and a radius, know the equation of the circle with that radius centered at that point, and vice versa: given an equation corresponding to a circle, recognize it as the equation of a circle, and determine its center and radius.
Problems & Challenges
- How close is the line \(y=3x+5\) from the origin? In general, how close is the line with equation \(y = mx+b\) to the origin?
- For any three non-colinear points in space, there is a unique circle that passes through though points. TK
- For any three non-colinear points in space, there is a unique parabola that passes through though points. TK How’s this relate to the circle?