Appendix
A-6: Coordinate Geometry
Example A-6.1
Obtain the slope, midpoint, length of the line segment, and equation of the line connecting the points −3,5 and 7,2.
Solution
Interactive Solution
Solution via Context Panel
Tools≻Load Package: Student Precalculus
Loading Student:-Precalculus
Slope
Context Panel: Student Precalculus≻Lines And Segments≻Slope
−3,5,7,2→slope through points−310
Midpoint
Context Panel: Student Precalculus≻Lines And Segments≻Midpoint
−3,5,7,2→midpoint of points2,72
Length of line segment (distance between endpoints)
Context Panel: Student Precalculus≻Lines And Segments≻Distance
−3,5,7,2→distance between points109
Equation of line
Context Panel: Student Precalculus≻Lines And Segments≻Line≻Equation
−3,5,7,2→equation of liney=−310x+4110
There are Task templates for each of these tasks, obtained with the following paths:
Tools≻Tasks≻Browse: Algebra≻Line Segment - Slope
Tools≻Tasks≻Browse: Algebra≻Line Segment - Midpoint
Tools≻Tasks≻Browse: Algebra≻Distance between Two Points
Tools≻Tasks≻Browse: Algebra≻Equation of a Line≻Two-Point
In addition there are Task templates for the point-slope and slope-intercept forms of the straight line:
Tools≻Tasks≻Browse: Algebra≻Equation of a Line≻Point - Slope
Tools≻Tasks≻Browse: Algebra≻Equation of a Line≻Slope - Intercept
For example, with the template for the distance between two points, we obtain
Distance between Two Real Points
Enter points as lists or vectors:
Point 1:
Point 2:
=
Similarly, with the template for the equation of a line through two points, we obtain
Compute the Equation of the Line Passing through 2 Points
Enter the first point:
−3,5
Enter the second point:
7,2
Compute the equation of the line passing through the two points:
StudentPrecalculusLine,1
y=−310x+4110
The functionality of the Line command is captured in the tutor in the Precalculus grouping of tutors. Figure A-6.1(a) provides a screenshot of the Line tutor initialized for this example.
Figure A-6.1(a) Line tutor initialized for this example
Coded Solution
The Student Precalculus package has commands for each of these:
StudentPrecalculusSlope−3,5,7,2
StudentPrecalculusMidpoint−3,5,7,2
Distance
StudentPrecalculusDistance−3,5,7,2
Line
StudentPrecalculusLine−3,5,7,21
Notice the required [1] at the end of the Line command. Instead, [2] will give the slope while [3] and [4] will give the x- and y-intercepts, respectively. The arguments of the Line command can also be a point and the slope, or the slope and y-intercept, as done in the next example.
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