If (xi ,yi),i=1,2,3, are the vertice...

If `(x_i ,y_i),i=1,2,3,` are the vertices of an equilateral triangle such that `(x_1+2)^2+(y_1-3)^2=(x_2+2)^2+(y_2-3)^2=(x_3+2)^2+(y_3-3)^2,` then find the value of `(x_1+x_2+x_3)/(y_1+y_2+y_3)` .

Text Solution

AI Generated Solution

Topper's Solved these Questions

COMPLEX NUMBERS
CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|9 Videos
CONTINUITY AND DIFFERENTIABILITY
CENGAGE ENGLISH|Exercise Comprehension Type|2 Videos

Similar Questions

Explore conceptually related problems

If A(x_1,y_1),B(x_2,y_2) and C(x_3,y_3) are the vertices of traingle ABC and x_(1)^(2)+y_(1)^(2)=x_(2)^(2)+y_(2)^(2)=x_3^(2)+y_(3)^(2) , then show that x_1 sin2A+x_2sin2B+x_3sin2C=y_1sin2A+y_2sin2B+y_3sin 2C=0 .

The sides of an equilateral triangles are given by x+ 3y , 3x+ 2y - 2 and 4x + (1)/(2) y+ 1

Write the formula for the area of the triangle having its vertices at (x_1,\ y_1),\ \ (x_2,\ y_2) and (x_3,\ y_3) .

If the coordinates of the vertices of an equilateral triangle with sides of length a are (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) then |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2=(3a^(4))/4

If A(x_1, y_1),B(x_2, y_2)a n dC(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |(x_1,y_1, 2),(x_2,y_2, 2),(x_3,y_3, 2)|^2=3a^4

If (x_1-x_2)^2+(y_1-y_2)^2=a^2 , (x_2-x_3)^2+(y_2-y_3)^2=b^2 , (x_3-x_1)^2+(y_3-y_1)^2=c^2 , and 2s=a+b+c then what willl be the value of 1/4|[x_1,y_1, 1],[x_2,y_2, 1],[x_3,y_3, 1]|^2

If A (x_(1), y_(1)), B (x_(2), y_(2)) and C (x_(3), y_(3)) are vertices of an equilateral triangle whose each side is equal to a, then prove that |(x_(1),y_(1),2),(x_(2),y_(2),2),(x_(3),y_(3),2)| is equal to

Find the value of x , if [(3x+y,-y),(2y-x,3)]=[(1, 2),(-5, 3)] .

If A(x_1, y_1),B(x_2, y_2) and C(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=3a^4

Show that the coordinates off the centroid of the triangle with vertices A(x_1, y_1, z_1),\ B(x_2, y_2, z_2)a n d\ (x_3, y_3, z_3) are ((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3,(z_1+z_2+z_3)/3)

CENGAGE ENGLISH-CONIC SECTIONS-All Questions

In what ratio does the x-axis divide the line segment joining the po...
Text Solution
|
If (1,4) is the centroid of a triangle and the coordinates of its a...
Text Solution
|
If (xi ,yi),i=1,2,3, are the vertices of an equilateral triangle s...
Text Solution
|
A particle just clears a wall of height b at distance a and strikes...
Text Solution
|
Find the locus of a point, so that the join of (-5,1) and (3,2) subten...
Text Solution
|
The sum of the squares of the distances of a moving point from two ...
Text Solution
|
A B is a variable line sliding between the coordinate axes in such ...
Text Solution
|
A rod of length l slides with its ends on two perpendicular lines. ...
Text Solution
|
Find the locus of the point (t^2-t+1,t^2+t+1),t in R.
Text Solution
|
Find the locus of a point such that the sum of its distance from the...
Text Solution
|
Two points P(a,0) and Q(-a,0) are given. R is a variable point on o...
Text Solution
|
If the coordinates of a variable point P are (acostheta,bsintheta), wh...
Text Solution
|
Find the locus of a point whose distance from (a, 0) is equal to it...
Text Solution
|
The coordinates of the point A and B are (a,0) and (-a ,0), respecti...
Text Solution
|
The locus of the foot of perpendicular drawn from origin to a variabl...
Text Solution
|
A variable line through the point P(2,1) meets the axes at A an d B...
Text Solution
|
If A(cosalpha,sinalpha),B(sinalpha,-cosalpha),C(1,2) are the vertic...
Text Solution
|
Let A(2,-3) and B(-2,1) be the vertices of Delta A B Cdot If the ...
Text Solution
|
Convert the following points from polar coordinates to the correspon...
Text Solution
|
A straight line is drawn through P(3,4) to meet the axis of x and y...
Text Solution
|