Advertisements
Advertisements
Question
If (−2, 1) is the centroid of the triangle having its vertices at (x , 0) (5, −2), (−8, y), then x, y satisfy the relation
Options
3x + 8y = 0
3x − 8y = 0
8x + 3y = 0
8x = 3y
None of these
Advertisements
Solution
We have to find the unknown co-ordinates.
The co-ordinates of vertices are A(x , 0) ; B(5,-2) ; C (-8, y)
The co-ordinate of the centroid is (−2, 1)
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,
`(-2 , 1) = ((x + 5 -8)/3 , (y - 2) /3)`
Compare individual terms on both the sides-
`(x - 3) /3 = -2`
So,
x = -3
Similarly,
`(y - 2) /3 = 1`
So,
y = 5
It can be observed that (x, y) = (−3, 5) does not satisfy any of the relations 3x + 8y = 0, 3x − 8y = 0, 8x + 3y = 0 or 8x = 3y.
APPEARS IN
RELATED QUESTIONS
Which point on the x-axis is equidistant from (5, 9) and (−4, 6)?
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
The points A(2, 0), B(9, 1) C(11, 6) and D(4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.
If the coordinates of the mid-points of the sides of a triangle be (3, -2), (-3, 1) and (4, -3), then find the coordinates of its vertices.
Determine the ratio in which the point P (m, 6) divides the join of A(−4, 3) and B(2, 8). Also, find the value of m.
If the point C ( - 2,3) is equidistant form the points A (3, -1) and Bx (x ,8) , find the value of x. Also, find the distance between BC
Show that the following points are the vertices of a rectangle
A (0,-4), B(6,2), C(3,5) and D(-3,-1)
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, −3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.
Show that `square` ABCD formed by the vertices A(-4,-7), B(-1,2), C(8,5) and D(5,-4) is a rhombus.
The measure of the angle between the coordinate axes is
The ordinate of any point on x-axis is
If P ( 9a -2 , - b) divides the line segment joining A (3a + 1 , - 3 ) and B (8a, 5) in the ratio 3 : 1 , find the values of a and b .
If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.
If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c.
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.
If points Q and reflections of point P (−3, 4) in X and Y axes respectively, what is QR?
The distance of the point (4, 7) from the x-axis is
If points A (5, p) B (1, 5), C (2, 1) and D (6, 2) form a square ABCD, then p =
If the line segment joining the points (3, −4), and (1, 2) is trisected at points P (a, −2) and Q \[\left( \frac{5}{3}, b \right)\] , Then,
The point whose ordinate is 4 and which lies on y-axis is ______.
