Straight Lines

Question 1

What are Polar coordinates x=? And y=?

Answer 1

x= r cos #
y= r sin #

Question 2

What is Centroid of a triangle coordinates

Answer 2

(x,y)= (x1+x2+x3/3,y1+y2+y3/3)

Question 3

What are the coordinates of circumcentre of triangle ?

Answer 3

x= ( x1 sin 2A+ x2 sin 2B + x3 sin 2C/ sin 2A+sin 2B+ sin 2C)
Circumcentre O is the mid point of hypotenuse.

Question 4

What is Incentre of triangle coordinates

Answer 4

(x,y)= ( ax1+bx2+ cx3/a+b+c, ay1+by2+cy3/ a+b+c)

Question 5

What is Third vertex of an equilateral triangle coordinates

Answer 5

(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

Question 6

What is Angle between two straight lines

Answer 6

tan #= m2-m1/ 1+ m1m2

Question 7

What is Slope in intercept form y=?

Answer 7

y=mx+c

Question 8

What is Slope in one point form

(y-y1)=?

Answer 8

(y-y1)=m(x-x1)

Question 9

What is Intercept form where a is intercept made by straight line on x axis and b on y axis ?

Answer 9

x/a+ y/b= 1

Question 10

What is General eq of a straight line

Answer 10

Ax+ By+ c=0

Question 11

What is Eq of a straight line in normal form

Answer 11

x cos α + y sin α= p

Question 12

What is Eq of a straight line in parametric form

Answer 12

x-x1/cos #= y-y1/sin #= r

Question 13

What is Point of intersection of two straight lines coordinates

Answer 13

(x,y)= (b1c2-c2b1/a1b2-a2b1, c1a2-c2a1/a1b2-a2b1)

Question 14

What is Condition for two points to be on the same side of line

Answer 14

(ax1+by1+c)(ax2+by2+c)>0

Question 15

What is Eq of a straight line parallel to ax+by+c=0

Answer 15

ax+by+λ=0

Question 16

What is Eq of a line perpendicular to ax+by+c=0

Answer 16

bx-ay+λ=0

Question 17

What is Image of a point with respect to a line

Answer 17

x2-x1/a= y2-y1/b= -2(ax1+by1+c)/ a^+b^

Question 18

What is Length of perpendicular from a point to a line

Answer 18

l= |ax1+by1+c/ √a²+b²|

Question 19

What is Eq of family of lines passing through the intersection of two lines

Answer 19

(ax1+b1y+c1)+λ(a2x+b2y+c2)=0

Question 20

Write the stair method for calculating the area of triangle and also polygons

Answer 20

check book for answer buddy

Question 21

what is the formula for external division of Section formula

Answer 21

x=mx2-nx1/m-n

y=my2-ny1/m-n

Question 22

in questions for calculating the ratio in section formula, what’s the general convenient formula for writing the ratio (k method)?

Answer 22

take ratio k:1 and the apply formula

(kx2+x1/k+1,ky2+y1/k+1)= k:1

Question 23

what is centroid of a triangle

Answer 23

centroid of Triangle is the point of concurrency of the medians of a Triangle
(x1+x2+x3/3,y1+y2+y3/3)

Question 24

what is the incentre of a triangle

Answer 24

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)

Question 25

what is the circumcenter of a triangle

Answer 25

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 )

Question 26

what is the orthocentre of a triangle

Answer 26

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)

Question 27

in which type of triangle centroid orthocentre incentre and circumcentre lie on the same line

Answer 27

Isosceles triangle

Question 28

in which type of triangle centroid orthocentre incentre and circumcentre coincides

Answer 28

equilateral triangle

Question 29

Convert polar coordinates to rectangular

Answer 29

x=r cos x | y= r sin x

Question 30

convert rectangular coordinates to polar coordinates

Answer 30

tan x = y/x | r^2= x^ + y2