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Chapter 5 and 8: Coordinate Geometry of St. Lines (Equation of special…
Chapter 5 and 8: Coordinate
Geometry of St. Lines
Distance Formula
AB^2 = (x2-x1)^2 + (y2-y1)^2
Perpendicular
If L1 is perpendicular to L2, then slope of L1 x slope of L2 = -1
If slope of L1 x slope of L2 = -1, then L1 is perpendicular to L2
St. Lines passing through the origin
Slope intercept form, y=slope(x)+0
since (0,0)
therefore, y=slope(x)
Slope Formula
slope = y2-y1/x2-x1
Slope going upwards from left to right > 0
Slope going downwards from left to right < 0
Slope of horizontal line is 0
Slope of a vertical line is undefined
Inclination
Slope of L = tanΘ
Measured anti-clockwise from the x-axis to L
Parallel
If L1//L2, then slope of L1=slope of L2
If slope of L1=slope of L2, then L1//L2
Mid-point Formula
x=(x1+x2 /2), y=(y1+y2 /2)
Section formula for internal division
A(x1,y2), B(x2,y2), P(x,y) and AP:PB = r:s
x= sx1+rx2 /r+s, y= sy1+ry2 /r+s
Equation of St. Line by point-slope form
y-y1/x-x1=slope
Slope-intercept form
y=slope(x)+0
General form
x-y=0
Equation using two points
Step 1, Find the slope. Step 2, Apply the Point-slope form.
y-y1/x-1 = y2-y1/x2-x1
Equation of special straight lines
Horizontal
y2-y1/x2-x1=0
y= y-intercept
Vertical
y2-y1/x2-x1=slope
x= x-intercept