RMB DAV CENTENARY PUBLIC SCHOOL NAWANSHAHR | |||||
NAME OF THE TEACHER | DINESH KUMAR | ||||
CLASS | XI | CHAPTER | 10 | SUBJECT | MATHEMATICS |
TOPIC | STRAIGHT LINES | DURATION : 20 Class Meetings | |||
S. No.
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Topic
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1
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Introduction: In earlier classes we have studied
about the coordinate geometry. Coordinate geometry is the combination of
algebra and geometry.
Teacher should explain the following
formulas of coordinate geometry: Distance formula, section formula, mid - point
formula, area of triangle, centroid of triangle and collinearity of three
points.
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2
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Now teacher should explain the method of
shifting the origin. How equation of line changes when the origin is shifted
from one point to another.
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3
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Angle of inclination of a line: The angle θ made by the line l with positive direction of x-axis and
measured anti clockwise is called the inclination of the line. Where 0o ≤ θ ≤ 180o .
Angle of inclination of x-axis or any line parallel to x-axis is always 0o.
Angle of inclination of y-axis or any
line parallel to y-axis is always 90o.
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4
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Slope of a line : If θ is the angle of
inclination of a line then tanθ is called the slope
of the line. Slope of a line is denoted by m. Slope of x-axis is zero and the
slope of y-axis is not-defined.
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5
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Slope of a line
passing through two points
Let P(x1,
y1), P(x2, y2) are two point on the line,
then
* If slope of any line is
m1, then slope of any line perpendicular
to it is (m2)= -1/m , or
* Two lines are
perpendicular to each other if product of their slopes is =-1
* Or Two lines are
perpendicular to each other if : m1
x m2 = -1
* Two lines are parallel
if their slopes are equal.
* Three points A, B, C
are said to be collinear if
Slope of AB = Slope of
BC = Slope of AC
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6
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Angle between two lines:
If m1
and m2 are the slopes of two
lines intersecting each other at a point, then angle between them is given by
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7
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Various forms of
equation of line:
Equation of the form y = b, or y = -b is a line parallel to the
x – axis.
Equation of the form x = a, or x = -a is a line parallel to the
y – axis.
Point Slope form of
equation of the line
Equation of the line passing through
the point P(x1, y1) and having slope m is given by Y - y1 =
m(x - x1)
Two Point form of equation
of line
Equation of the line passing through
the two points P(x1, y1)
and Q(x2, y2)
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8
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Slope Intercept form of equation of
line
If a line have slope m and y
intercept c then equation of the line is
Y – c = m(x – 0) or
y = mx + c
If a line have slope m and x
intercept d then equation of the line
is
Y -0 = m(x-d) or
y = m(x – d)
Intercept form of equation of line
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9
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Normal form of equation of line
: xcosθ + ysinθ = p
* Where p is the perpendicular distance
of the line from the origin.
* Perpendicular distance of the line
from the origin is called Normal.
* θ is the angle made by the normal with the
positive direction of x – axis.
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10
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General Equation of the line
An equation of the form Ax + By + C = 0 is called general equation
of line. Where A and B are not zero simultaneously.
This general equation of the line can
be converted into all the forms of equation of line. Teacher should explain
all the forms on by one to the student.
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11
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Distance of a line Ax + By + C = 0, from a point (x1, y1)
is given by
Teacher should help the students in the
implementation of all these formulas in different problems.
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