Advertisements
Advertisements
प्रश्न
If the centroid of the triangle formed by the points (3, −5), (−7, 4), (10, −k) is at the point (k −1), then k =
विकल्प
3
1
2
4
Advertisements
उत्तर
We have to find the unknown co-ordinates.
The co-ordinates of vertices are
A (3,-5) ; B (-7,4) ; C (10, -k)
The co-ordinate of the centroid is (k , - 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,
`(k , -1) = ((3-7+10)/3 ,(-5+4-k)/3)`
Compare individual terms on both the sides-
k = 2
APPEARS IN
संबंधित प्रश्न
In Fig. 14.36, a right triangle BOA is given C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A and B.
We have a right angled triangle,`triangle BOA` right angled at O. Co-ordinates are B (0,2b); A (2a, 0) and C (0, 0).
Find a point on y-axis which is equidistant from the points (5, -2) and (-3, 2).
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by y-axis. Also, find the coordinates of the point of division in each case.
The line segment joining A( 2,9) and B(6,3) is a diameter of a circle with center C. Find the coordinates of C
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
The abscissa of a point is positive in the
In \[∆\] ABC , the coordinates of vertex A are (0, - 1) and D (1,0) and E(0,10) respectively the mid-points of the sides AB and AC . If F is the mid-points of the side BC , find the area of \[∆\] DEF.
If \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and } F\left( \frac{7}{2}, \frac{7}{2} \right)\] are the mid-points of sides of \[∆ ABC\] , find the area of \[∆ ABC\] .
If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
Find the value of a so that the point (3, a) lies on the line represented by 2x − 3y + 5 = 0
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.
If the distance between the points (4, p) and (1, 0) is 5, then p is equal to ______.
The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.
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 (–6, 8) from x-axis is ______.
