Straight Lines Flashcards
What are Polar coordinates x=? And y=?
x= r cos # y= r sin #
What is Centroid of a triangle coordinates
(x,y)= (x1+x2+x3/3,y1+y2+y3/3)
What are the coordinates of circumcentre of triangle ?
x= ( x1 sin 2A+ x2 sin 2B + x3 sin 2C/ sin 2A+sin 2B+ sin 2C)
Circumcentre O is the mid point of hypotenuse.
What is Incentre of triangle coordinates
(x,y)= ( ax1+bx2+ cx3/a+b+c, ay1+by2+cy3/ a+b+c)
What is Third vertex of an equilateral triangle coordinates
(x,y)= (x1+x2±√3(y1-y2)÷2,y1+y2±√3(x1-x2)÷2)
;(x1,y1)(x2,y2) are vertices of equilateral triangle and (x,y) is third vertex of equilateral triangle
What is Angle between two straight lines
tan #= m2-m1/ 1+ m1m2
What is Slope in intercept form y=?
y=mx+c
What is Slope in one point form
(y-y1)=?
(y-y1)=m(x-x1)
What is Intercept form where a is intercept made by straight line on x axis and b on y axis ?
x/a+ y/b= 1
What is General eq of a straight line
Ax+ By+ c=0
What is Eq of a straight line in normal form
x cos α + y sin α= p
What is Eq of a straight line in parametric form
x-x1/cos #= y-y1/sin #= r
What is Point of intersection of two straight lines coordinates
(x,y)= (b1c2-c2b1/a1b2-a2b1, c1a2-c2a1/a1b2-a2b1)
What is Condition for two points to be on the same side of line
(ax1+by1+c)(ax2+by2+c)>0
What is Eq of a straight line parallel to ax+by+c=0
ax+by+λ=0
What is Eq of a line perpendicular to ax+by+c=0
bx-ay+λ=0
What is Image of a point with respect to a line
x2-x1/a= y2-y1/b= -2(ax1+by1+c)/ a^+b^
What is Length of perpendicular from a point to a line
l= |ax1+by1+c/ √a²+b²|
What is Eq of family of lines passing through the intersection of two lines
(ax1+b1y+c1)+λ(a2x+b2y+c2)=0
Write the stair method for calculating the area of triangle and also polygons
check book for answer buddy
what is the formula for external division of Section formula
x=mx2-nx1/m-n
y=my2-ny1/m-n
in questions for calculating the ratio in section formula, what’s the general convenient formula for writing the ratio (k method)?
take ratio k:1 and the apply formula
(kx2+x1/k+1,ky2+y1/k+1)= k:1
what is centroid of a triangle
centroid of Triangle is the point of concurrency of the medians of a Triangle
(x1+x2+x3/3,y1+y2+y3/3)
what is the incentre of a triangle
the point of concurrency of the internal bisectors of the angles of a triangle is called in centre of a triangle
(ax1+bx2+cx3/a+b+c,ay1+by2+cy3/a+b+c)
what is the circumcenter of a triangle
circumcenter is the point which is equidistant from the vertices of a triangle
( x1 sin 2A + x2 sin 2B +x3 sin 2C/sin 2A+ sin 2B + sin 2C, y1 sin 2A + y2 sin 2B + y3 sin 2C/sin 2A + sin 2B + sin 2C )
what is the orthocentre of a triangle
the point of concurrency of the altitude of a triangle is called the orthocenter of a triangle
(x1 tan A+ x2 tan B + x3 tan C/ tan A + tan B+ tan C, y1 tan A + y2 tan B + y3 tan C/ tan A+ tan B + tan C)
in which type of triangle centroid orthocentre incentre and circumcentre lie on the same line
Isosceles triangle
in which type of triangle centroid orthocentre incentre and circumcentre coincides
equilateral triangle
Convert polar coordinates to rectangular
x=r cos x
y= r sin x
convert rectangular coordinates to polar coordinates
tan x = y/x
r^2= x^ + y2
