Advertisements
Advertisements
प्रश्न
Find the third vertex of a triangle, if two of its vertices are at (−3, 1) and (0, −2) and the centroid is at the origin.
Advertisements
उत्तर
We have to find the co-ordinates of the third vertex of the given triangle. Let the co-ordinates of the third vertex be(x,y).
The co-ordinates of other two vertices are (−3, 1) and (0, −2)
The co-ordinate of the centroid is (0, 0)
We know that the co-ordinates of the centroid of a triangle whose vertices are
`(x_1,y_1),(x_2,y_2),(x_3,y_3)`is
`((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`
So,
`(0,0)=((x+0-0)/3,(y+1-2)/3)`
Compare individual terms on both the sides-
`(x-3)/3=0`
So,
x=3
Similarly,
`(y-1)/3=0`
So,
y=1
So the co-ordinate of third vertex (3,1)
APPEARS IN
संबंधित प्रश्न
How will you describe the position of a table lamp on your study table to another person?
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
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 points p (x , y) is point equidistant from the points A (5,1)and B ( -1,5) , Prove that 3x=2y
If p(x , y) is point equidistant from the points A(6, -1) and B(2,3) A , show that x – y = 3
Show that the following points are the vertices of a square:
A (0,-2), B(3,1), C(0,4) and D(-3,1)
Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that `(PA)/( PQ)=2/5` . If that point A also lies on the line 3x + k( y + 1 ) = 0, find the value of k.
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
The co-ordinates of point A and B are 4 and -8 respectively. Find d(A, B).
Find the value of a for which the area of the triangle formed by the points A(a, 2a), B(−2, 6) and C(3, 1) is 10 square units.
Find the value(s) of k for which the points (3k − 1, k − 2), (k, k − 7) and (k − 1, −k − 2) are collinear.
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.
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is
The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be
Find the coordinates of the point of intersection of the graph of the equation x = 2 and y = – 3
If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has ______.
