Advertisements
Advertisements
Question
Determine the ratio in which the straight line x - y - 2 = 0 divides the line segment
joining (3, -1) and (8, 9).
Solution
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
RELATED QUESTIONS
How will you describe the position of a table lamp on your study table to another person?
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.
Find a point on y-axis which is equidistant from the points (5, -2) and (-3, 2).
Find the points of trisection of the line segment joining the points:
5, −6 and (−7, 5),
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
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.
ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of one its diagonal.
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
Find the ratio in which the line segment joining the points A(3, 8) and B(–9, 3) is divided by the Y– axis.
Find the value of k if points A(k, 3), B(6, −2) and C(−3, 4) are collinear.
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.
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
If points Q and reflections of point P (−3, 4) in X and Y axes respectively, what is QR?
Find the values of x for which the distance between the point P(2, −3), and Q (x, 5) is 10.
What is the distance between the points \[A\left( \sin\theta - \cos\theta, 0 \right)\] and \[B\left( 0, \sin\theta + \cos\theta \right)\] ?
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
In which quadrant does the point (-4, -3) lie?
Points (1, –1) and (–1, 1) lie in the same quadrant.
