Advertisements
Advertisements
प्रश्न
Determine the ratio in which the straight line x - y - 2 = 0 divides the line segment
joining (3, -1) and (8, 9).
उत्तर
Let the line x - y - 2 = 0 divide the line segment joining the points A (3,−1) and B (8, 9) in the ratio λ:1 at any point P(x,y)
Now according to the section formula if point a point P divides a line segment joining `A (x_1, y_1)` and `B(x_2,y_2)` the ratio m: n internally than.
`P(x,y)= ((nx_2 + mx_2)/(m + n), (ny_1 + my_2)/(m + n))`
So,
`P(x,y) = ((8y + 3)/(lambda + 1), (9lambda - 1)/(lambda+ 1))`
Since, P lies on the given line. So,
x - y - 2 =0
Put the values of co-ordinates of point P in the equation of line to get,
`((8lambda + 3)/(lambda + 1)) - ((9lambda- 1)/(lamda + 1)) - 2 = 0`
On further simplification we get,
`-3lambda + 2 = 0`
So, `lambda =2/3`
So the line divides the line segment joining A and B in the ratio 2: 3 internally.
APPEARS IN
संबंधित प्रश्न
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.
If the point A (4,3) and B ( x,5) lies on a circle with the centre o (2,3) . Find the value of x.
Show that the following points are the vertices of a rectangle.
A (2, -2), B(14,10), C(11,13) and D(-1,1)
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
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).
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).
ABCD is a parallelogram with vertices \[A ( x_1 , y_1 ), B \left( x_2 , y_2 \right), C ( x_3 , y_3 )\] . Find the coordinates of the fourth vertex D in terms of \[x_1 , x_2 , x_3 , y_1 , y_2 \text{ and } y_3\]
\[A\left( 6, 1 \right) , B(8, 2) \text{ and } C(9, 4)\] are three vertices of a parallelogram ABCD . If E is the mid-point of DC , find the area of \[∆\] ADE.
what is the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\] .
Write the coordinates of a point on X-axis which is equidistant from the points (−3, 4) and (2, 5).
The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio.
If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =
If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
The point whose ordinate is 4 and which lies on y-axis is ______.
Point (3, 0) lies in the first quadrant.
