Definitions [3]
Locus is the path traced by a moving point, which moves so as to satisfy a certain given condition/conditions.
The slope m of a line is m = tanθ
where θ is the inclination of the line with the positive x-axis.
An equation of the form ax + by + c = 0 represents a straight line and is known as a linear equation.
Formulae [4]
\[m=\frac{y_2-y_1}{x_2-x_1}\]
When slope and y-intercept are given
y = mx + c
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m = slope
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c = y-intercept (value of y when x = 0)
When two points are given
\[\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\]
When the slope and one point are given
y − y1 = m(x − x1)
Key Points
Nature of Slope
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m > 0 → rising line
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m < 0 → falling line
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m = 0 → horizontal line
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m = ∞→ vertical line
Parallel Lines
Two lines are parallel ⇔ , their slopes are equal, m1 = m2
Perpendicular Lines
Two lines are perpendicular ⇔
Collinearity of Three Points
Points A, B, and C are collinear
Method 1: Distance method
AB + BC = AC
Method 2: Slope method
Slope of AB = Slope of BC
