Straight Lines
Class 11 · Mathematics
4 ideas in Class 11 Mathematics, explained in plain words, with games and quizzes to practise.
Slope and Inclination
Part of: Slope and Line Forms
Slope equals tan of inclination; two-point slope divides rise by run; horizontal gives zero, vertical stays undefined; parallel lines share slopes.
Why it matters. Slope steers every line. Rise-over-run predicts direction.
Formulas
- m = tan(inclination)
- m = (y2 - y1) / (x2 - x1)
- Parallel lines share the same slope
Key words
- Inclination
- : The angle a line makes with the positive x-axis, from 0 to 180 degrees.
- Slope
- : The steepness of a line, equal to rise over run.
- Zero slope
- : A flat line with slope zero.
- Undefined slope
- : A vertical line whose slope cannot be computed.
Try it in two minutes
- Read the inclination.
- Divide rise by run.
- Match parallel slopes.
Try at home. Measure a staircase slope.
Forms of Straight Lines
Part of: Slope and Line Forms
Point-slope anchors at one point; two-point spans pairs; slope-intercept splits m and c; intercept form divides by a and b; normal form uses p and angle.
Why it matters. Each form fits given data. Conversion unifies lines.
Formulas
- Point-slope: y - y1 = m(x - x1)
- Slope-intercept: y = mx + c
- Intercept form: x/a + y/b = 1
Key words
- Point-slope form
- : Line through (x1, y1) with slope m, in point-slope dress.
- Two-point form
- : Line through two given points.
- Slope-intercept form
- : Line with slope m cutting the y-axis at c.
- Intercept form
- : Line cutting the axes at a and b.
- Normal form
- : Line fixed by its perpendicular distance p from origin.
Try it in two minutes
- Pick the fitting form.
- Substitute the data.
- Simplify to general.
Try at home. Write your street as y = mx + c.
Parallel Perpendicular and Concurrency
Part of: Relations and Distance
Parallel shares slopes; perpendicular multiplies to minus-one; angle formula reads tan of slope gaps; concurrency zeroes the three-row determinant; families add lambda-times-second-line.
Why it matters. Relations classify line pairs. Concurrency tests meetings.
Formulas
- Perpendicular lines: m1 x m2 = -1
- tan(angle) = |(m2 - m1) / (1 + m1 x m2)|
- Concurrency: the three-line determinant is zero
Key words
- Perpendicular lines
- : Two lines meeting at a right angle.
- Angle between lines
- : The acute turn from one line to another.
- Concurrency
- : Three or more lines passing through one common point.
- Family of lines
- : All lines through one point, written as first line + k x second line.
Try it in two minutes
- Compare slopes.
- Multiply for right angles.
- Test the determinant.
Try at home. Check notebook rulings for parallel.
Distance of Lines and Points
Part of: Relations and Distance
Point-to-line divides absolute-substitution by root-a-squared-b-squared; parallels divide constant-gap by same root; foot and image mirror across lines.
Why it matters. Distances size corridors. Feet project points.
Formulas
- d = |a x1 + b y1 + c| / root(a^2 + b^2)
- Parallels y = mx + c1 and c2: gap = |c1 - c2| / root(1 + m^2)
Key words
- Perpendicular distance
- : The shortest segment from a point to a line, meeting it at 90 degrees.
- Foot of perpendicular
- : The point where the perpendicular from a point meets the line.
- Image of a point
- : The mirror point of a given point across a line.
- Distance between parallels
- : The constant gap between two parallel lines.
Try it in two minutes
- Substitute the point.
- Divide by the root.
- Gap constants for parallels.
Try at home. Measure book edge to table line.
What your child will practise
- Distance of Lines and Points: Candy Puzzle (Clue Puzzle)
- Distance of Lines and Points: Candy Quick Fire (Quick Fire)
- Forms of Straight Lines: Desert Puzzle (Clue Puzzle)
- Parallel Perpendicular and Concurrency: Space Quest (Flip and Match)
- Slope and Inclination: Ocean Quick Fire (Quick Fire)
- Quiz: Distance of Lines and Points (8 questions)
- Quiz: Forms of Straight Lines (8 questions)
- Quiz: Parallel Perpendicular and Concurrency (8 questions)
- Quiz: Slope and Inclination (8 questions)