Coordinate Geometry | Mathematics - Points to Remember | 10th Mathematics : UNIT 5 : Coordinate Geometry
Chapter: 10th Mathematics : UNIT 5 : Coordinate Geometry
Points to Remember
Points to
Remember
·
The
area of a triangle formed by the points (x1
, y1 ) , (x2 , y2 ) and (x3 , y3
) is 1/2 { (x1y2 + x2y3 + x3 y1) − (x2y1 + x3y2 + x1y3) } sq.units
·
Three
points A(x1,y1),B(x2,y2)
and C(x3,y3) are collinear if and only if
(i)
area of ΔABC = 0 or x1y2
+ x2y3 + x3y1 = x2y1
+ x3y2 + x1y3
(ii)
slope of AB = slope of BC or slope of AC
·
The
area of a quadrilateral formed by the four points (x1
, y1 ) , (x2 , y2 ), (x3 , y3
) and (x4 , y4 )is
1/2 { (x1y2 + x2y3 + x3 y4+ x4 y1) − (x2y1 + x3y2 + x4y3+ x1y4) } sq.units
·
If
a line makes an angle θ with the positive direction of X axis, then its slope m = tanθ.
·
If
A(x1,y1), B(x2,y2) are two distinct
points then the slope of AB is (y2
- y1) / (x2 - x1).
·
Slope
of line ax+by+c= 0 is m = − a/b.
Equation of straight line in various
forms
·
Two
straight lines are parallel if and only if their slopes are equal.
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