Unit 8: Characteristics of Linear Relations (Math 10C)
Line segments, distance & midpoint, slope, and parallel & perpendicular lines.
Slope \(m=\dfrac{y_2-y_1}{x_2-x_1}\)
Distance \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Midpoint \(M\!\left(\tfrac{x_1+x_2}{2},\tfrac{y_1+y_2}{2}\right)\)
Parallel: \(m_1=m_2\)
Perpendicular: \(m_1m_2=-1\)
What You Should Be Able To Do
- Find slope from two points, tables, or graphs; identify horizontal/vertical lines.
- Calculate the distance and midpoint of a segment and sketch accurately.
- Write and convert linear equations: slope–intercept, point–slope, and standard forms.
- Determine lines parallel or perpendicular to a given line through a point.
Progress autosaves to this device.
Video Library
Slope from Two Points
Compute, interpret, special cases.
youtube.com – “how to find slope from two points”Distance & Midpoint Formulas
Coordinate geometry essentials.
youtube.com – “distance and midpoint formula”Equations of Lines
Slope–intercept & point–slope, converting forms.
youtube.com – “writing equations of lines point slope and slope intercept”Parallel & Perpendicular Lines
Slopes, through a given point.
youtube.com – “parallel and perpendicular lines from equations”Interactive Tools
Segment Analyzer
Line Builder
Parallel & Perpendicular Checker
General Form \(Ax+By+C=0\)
Slope from a Table (Is it Linear?)
Unit 8 Quizzes
Downloadable Review
Quick Practice Scratchpad
Try: Find slope, distance, and midpoint for \((2,-5)\) to \((-4,7)\). Write a line perpendicular to \(y=\tfrac{2}{3}x-1\) through \((3,-2)\).