Lines
Distance:
Distance on the real line distance between -2 and 5
Midpoint of an interval on a line midpoint of 
Trisect an interval on a line Trisect [-2, 14]
Distance in quadrant 1 (2,5) and (4,1)
Distance in quadrants 2 and 1 (-3,1) and (2,4)
Distance, irrational coordinate 
Midpoint of a line in quadrant 1 (1,4) and (5,3)
Midpoint of a line in quadrants 2 and 1 (-4,1) and (3,5)
Origin, distance, one coordinate given distance from (-2,y) to the origin is 6
Point, distance, one coordinate given distance from (x,4) to (-2,1) is 4
Points equidistant from 2 given points (3, 2); (-3, -4)
Quadrisect a line segment (-7, 5); (9, -7)
Lines and triangles:
Three points determine a right triangle
a (-1,2); b (4,-3); c (1,3)
Three points determine an isosceles triangle (-2,5); (-5,1); (-1,-2)
Three points determine a line (-3, 2); (1, 1); (9, 7)
Three points determine a triangle (-5, 2); (-2, 1); (3, -4)
Intersections:
x, y intercepts and parabola intercepts for 
Pt of int of a line and a centered parabola y = x2 and y = x + 2.
Points of intersection of a line and a parabola y = 4x - x2 and y = 4 - x.
Line through 2 points:
Slope of line through 2 points: Positive (2, -5) and (6, 4)
Slope of line through 2 points: Negative (-3, 2) and (2, -4)
Slope of line through 2 points: Slope = 0 (-2, 3) and (5, 3)
Slope of line through 2 points: Slope undefined (-3, -2) and (-3, 4)
Line through two points in quadrant1 (1,4) and (7,1)
Line through points in quadrants 3 and 1 (-1,-3) and (3,5)
Line through points in quadrants 2 and 4 (-3,1) and (5,-3)
Line through points in Q1: Horizontal (3, 2) and (7, 2),
Line through points in Q4: Horizontal (2, -5) and (4, -5),
Line through 2 points: fractional coordinates (3/4, 5/6) and (-1/2, 2/3)
Point-slope form of a line:
Point slope in quadrant 1 Through (1,3) with slope = 1/2
Point slope: on x-axis Through (2, 0) with slope = 2/3.
Point slope: Q2, slope undefined Through (-2, 5) with slope undefined.
Point slope through the origin Through (0, 0) with slope = 3.
Point slope: Q3 Through (-2, -5) with slope = 2/5
Point slope: on y-axis Through (0, -2) with slope = 3
Point slope: Q2, negative slope Through (-3, 4) with slope = -1/2.
Intercepts:
Positive y-intercept, slope: with y-intercept = 3 and slope = 2.
Negative y-intercept, pos. slope: with y-intercept = -2 and slope = 1/3.
Positive, fractional y-intercept, negative slope: with y-intercept = 4/3 and slope = -2/5.
Positive y-intercept, slope = 0: with y-intercept = 2 and slope = 0.
x-intercept, vertical line: with x-intercept = 2 and is vertical.
Positive x- and y-intercepts: with x-intercept = 3 and y-intercept = 2.
Negative x-intercept, positive y-intercept: with x-intercept = -2 and y-intercept = 1/3.
Positive x-intercept, negative y-intercept: with x-intercept = 4 and y-intercept = -3.
Negative x- and y-intercepts: with x-intercept = -4 and y-intercept = -5.
Equal intercepts, point in Q1: with equal intercepts and through the point (3,4).
Equal intercepts, point in Q2: with equal intercepts and through the point (-2, 1).
X-intercept = twice y-intercept, fractional coord of point: with x-intercept equal to twice the y_intercept and through the point (3/2, 1/2)
X-intercept = -y-intercept, point in Q2: with x-intercept equal to minus the y_intercept and through the point (-2, 3).
Parallel and perpendicular lines:
Line, point in q2, parallel to another line Thru (-2,5), parallel to 3x - y + 4 = 0
Line, point in q3, perpend. to another line Thru (-1,-3), perpend. to 2x + y - 4 = 0
Line, point in q1, perp. to a vert line : through (3, 2) and perpendicular to the line x = 1.
Line, point in q1, par. to a vert line: through (3, 2) and parallel to the line x = 1.
Line, point in q2, perp. to a hor line : through (-2, 1) and perpendicular to the line y = 2.
Line, point in q2, par. to a hor line: through (-2, 1) and parallel to the line y = 2.
3 points on a line via eq. of line : (-4, 2); (-1, 1); (8, -2)
3 points not on a line via eq. of line : (-5, -3); (-2, 1); (7, 8).