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
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
Find the points of trisection of the line segment joining the points:
(3, -2) and (-3, -4)
Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.
If the point ( x,y ) is equidistant form the points ( a+b,b-a ) and (a-b ,a+b ) , prove that bx = ay
ABCD is rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P,Q,R and S be the midpoints of AB, BC, CD and DA respectively, Show that PQRS is a rhombus.
The midpoint P of the line segment joining points A(-10, 4) and B(-2, 0) lies on the line segment joining the points C(-9, -4) and D(-4, y). Find the ratio in which P divides CD. Also, find the value of y.
Prove that the diagonals of a rectangle ABCD with vertices A(2,-1), B(5,-1) C(5,6) and D(2,6) are equal and bisect each other
Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.
The co-ordinates of point A and B are 4 and -8 respectively. Find d(A, B).
If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a), then prove that x + y = a + b.
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
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?
If A (1, 2) B (4, 3) and C (6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D.
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 + b3 + c3 =
If points A (5, p) B (1, 5), C (2, 1) and D (6, 2) form a square ABCD, then p =
If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______.
The distance of the point P(2, 3) from the x-axis is ______.
Points (1, – 1), (2, – 2), (4, – 5), (– 3, – 4) ______.
In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?
