Advertisements
Advertisements
प्रश्न
Determine the ratio in which the point (-6, a) divides the join of A (-3, 1) and B (-8, 9). Also, find the value of a.
Advertisements
उत्तर
The co-ordinates of a point which divided two points `(x_1,y_1)` and `(x_2,y_2)`internally in the ratio m:n is given by the formula,
`(x,y) = (((mx_2 + nx_1)/(m + n))"," ((my_2 + ny_1)/(m + n)))`
Let us substitute these values in the earlier mentioned formula.
`(-6, a) = (((m(-8) +n(-3))/(m + n))","((m(9) +n(1))/(m + n)))`
Equating the individual components we have
`-6 = (m(-8) + n(-3))/(m + n)`
`-6m - 6n = -8m - 3n`
2m = 3n
`m/n = 3/2`
We see that the ratio in which the given point divides the line segment is 3:2
Let us now use this ratio to find out the value of 'a'.
`(-6,a) = (((m(-8) + n(-3))/(m - n))","((m(9) + n(1))/(m + n)))`
`(-6, a) = (((3(-8) + 2(-3))/(3 + 2))"," ((3(9) + 2(1))/(3 + 2)))`
Equating the individual components we have
`a = (3(9) + 2(1))/(3 + 2)`
`a= 29/5`
Thus the vlaue of a is 29/5
APPEARS IN
संबंधित प्रश्न
If (−2, 3), (4, −3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.
Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus.
Also, find its area.
Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).
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
Find the centroid of ΔABC whose vertices are A(2,2) , B (-4,-4) and C (5,-8).
Show that `square` ABCD formed by the vertices A(-4,-7), B(-1,2), C(8,5) and D(5,-4) is a rhombus.
Points P, Q, R and S divides the line segment joining A(1, 2) and B(6, 7) in 5 equal parts. Find the coordinates of the points P, Q and R.
Find the value of k, if the points A (8, 1) B(3, −4) and C(2, k) are collinear.
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.
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 \[∆ ABC\] .
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
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.
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.
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
The point on the x-axis which is equidistant from points (−1, 0) and (5, 0) is
Any point on the line y = x is of the form ______.
In the above figure, seg PA, seg QB and RC are perpendicular to seg AC. From the information given in the figure, prove that: `1/x + 1/y = 1/z`
The point at which the two coordinate axes meet is called the ______.
The points (–5, 2) and (2, –5) lie in the ______.
