Advertisements
Advertisements
प्रश्न
If the centroid of the triangle formed by points P (a, b), Q(b, c) and R (c, a) is at the origin, what is the value of a + b + c?
उत्तर
The co-ordinates of the vertices are (a, b); (b, c) and (c, a)
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) = `((a + b+ c ) /3 , ( b+ c+ a ) / 3)`
Compare individual terms on both the sides-
`(a + b+ c) / 3 = 0`
Therefore,
a + b+ c = 0
APPEARS IN
संबंधित प्रश्न
How will you describe the position of a table lamp on your study table to another person?
The coordinates of the point P are (−3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.
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 points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?
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.
ΔXYZ ∼ ΔPYR; In ΔXYZ, ∠Y = 60o, XY = 4.5 cm, YZ = 5.1 cm and XYPY =` 4/7` Construct ΔXYZ and ΔPYR.
Prove hat the points A (2, 3) B(−2,2) C(−1,−2), and D(3, −1) are the vertices of a square ABCD.
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.
\[A\left( 6, 1 \right) , B(8, 2) \text{ and } C(9, 4)\] are three vertices of a parallelogram ABCD . If E is the mid-point of DC , find the area of \[∆\] ADE.
If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =
If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=
If P is a point on x-axis such that its distance from the origin is 3 units, then the coordinates of a point Q on OY such that OP = OQ, are
The coordinates of the circumcentre of the triangle formed by the points O (0, 0), A (a, 0 and B (0, b) are
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
The coordinates of the point P dividing the line segment joining the points A (1, 3) and B(4, 6) in the ratio 2 : 1 are
What is the form of co-ordinates of a point on the X-axis?
Ordinate of all points on the x-axis is ______.
Which of the points P(0, 3), Q(1, 0), R(0, –1), S(–5, 0), T(1, 2) do not lie on the x-axis?
The distance of the point (–1, 7) from x-axis is ______.
