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, determine 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, determine 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
- A football field is 160’ wide and 360’ long (remember the end zones). Suppose you have to walk from one corner of the football field to the opposite corner. How far is this? As a percentage, how much shorter is it to cut across the field diagonally rather than walk around the outside?
- What is the closest the line \(y=3x+5\) comes to the origin? In general, how close does the line with equation \(y = mx+b\) come to the origin?
- How far apart are the parallel lines \(y = \frac{1}{2}x + 3\) and \(y = \frac{1}{2}x + 8?\) In general, given to parallel lines \(y = mx + b_1\) and \(y = mx + b_2,\) how far apart are they?
- 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?