Explore the fundamentals of straight lines, including their equations, slopes, and various forms, to understand their properties and applications in geometry.
Straight Lines - Quick Look Revision Guide
Your 1-page summary of the most exam-relevant takeaways from Mathematics.
This compact guide covers 20 must-know concepts from Straight Lines aligned with Class 11 preparation for Mathematics. Ideal for last-minute revision or daily review.
Complete study summary
Essential formulas, key terms, and important concepts for quick reference and revision.
Key Points
Slope (m) & its definition.
Slope is defined as m = tan(θ) where θ is the angle with the x-axis.
Distance between points formula.
Distance PQ = √[(x2 - x1)² + (y2 - y1)²]. Essential for calculating distances.
Slope of a line through two points.
For points (x1, y1) and (x2, y2), m = (y2 - y1) / (x2 - x1).
Conditions for parallel lines.
Two lines are parallel if and only if their slopes are equal. (m1 = m2).
Conditions for perpendicular lines.
Lines are perpendicular if m1 * m2 = -1. Slopes are negative reciprocals.
Equation of a line in point-slope form.
If slope m and point (x0, y0), then y - y0 = m(x - x0).
Slope-intercept form of a line.
y = mx + c, where m is the slope and c is the y-intercept.
Intercept form of a line.
If a and b are x-intercept and y-intercept, then the equation is x/a + y/b = 1.
Area of triangle formula.
Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | with vertices (x1,y1),(x2,y2),(x3,y3).
Condition for collinearity.
Points A, B, C are collinear if slope AB = slope BC.
Finding the midpoint.
Midpoint M of (x1, y1) and (x2, y2) is M = ((x1+x2)/2, (y1+y2)/2).
Distance from a point to a line.
Distance d = |Ax1 + By1 + C| / √(A² + B²) for line Ax + By + C = 0.
Equation of a vertical line.
Vertical line through (a, b) is x = a.
Equation of a horizontal line.
Horizontal line through (a, b) is y = b.
Finding slopes from angles.
If the line makes an angle α with the x-axis, then m = tan(α).
Equation for equal intercepts.
A line cutting equal intercepts on axes has the form x + y = k.
Gradient of a line.
A positive gradient indicates an upward slope, a negative one indicates downward.
Finding the equation from slope and point.
Using point (x1, y1) and slope m, the line's equation is y - y1 = m(x - x1).
Conditions for concurrent lines.
Three lines are concurrent if their pairwise intersection points lie on the third line.
Reflection across a line.
Image of point (x,y) across line is found using perpendicular lines for calculations.
Symmetry about axes.
If point (x,y) is reflected over both axes, the result is (-x,-y).
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