Advertisements
Advertisements
प्रश्न
Find the centroid of ΔABC whose vertices are A(2,2) , B (-4,-4) and C (5,-8).
Advertisements
उत्तर
The given points are A(2,2) , B (-4,-4) and C (5,-8).
`Here , (x_1 = 2, y_1=2), (x_2=-4, y_2=-4) and (x_3=5 , y_3 =-8)`
Let G (x ,y) br the centroid of Δ ABC Then ,
`x= 1/3 (x_1+x_2+x_3)`
`=1/2(2-4+5)`
=1
`y=1/3(y_1+y_2+y_3)`
`=1/3 (2-4-8)`
`=(-10)/3`
Hence, the centroid of ΔABC is G `(1,(-10)/3).`
APPEARS IN
संबंधित प्रश्न
Which point on the y-axis is equidistant from (2, 3) and (−4, 1)?
Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.
Find a point on y-axis which is equidistant from the points (5, -2) and (-3, 2).
Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and(1, 2) meet
Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).
If the point A (4,3) and B ( x,5) lies on a circle with the centre o (2,3) . Find the value of x.
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
Show that the following points are the vertices of a square:
A (0,-2), B(3,1), C(0,4) and D(-3,1)
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
Find the area of quadrilateral ABCD whose vertices are A(-3, -1), B(-2,-4) C(4,-1) and D(3,4)
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.
If the point P(x, 3) is equidistant from the point A(7, −1) and B(6, 8), then find the value of x and find the distance AP.
If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.
Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?
Find the value of a so that the point (3, a) lies on the line represented by 2x − 3y + 5 = 0
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?
