Advertisements
Advertisements
प्रश्न
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
Advertisements
उत्तर
Let P( x , 0 ) be the point of intersection of x-axis with the line segment joining A (2, 3) and B (3,−2) which divides the line segment AB in the ratio λ : 1 .
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 ) ` in the ratio m: n internally than,
`P (x , y) = ((nx_ 1+ mx_2 )/(m+n) ,(ny_1 + my_2) /(m + n ) )`
Now we will use section formula as,
`( x , 0 ) = ((3λ +2)/(λ +1) ,(3-2λ )/(λ + 1) )`
Now equate the y component on both the sides,
`(3-2λ )/(λ + 1) = 0`
On further simplification,
`λ = 3/2`
So x-axis divides AB in the ratio`3/2`
APPEARS IN
संबंधित प्रश्न
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when A coincides with the origin and AB and AD are along OX and OY respectively.
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
The line joining the points (2, 1) and (5, −8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0. Find the value of k.
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
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.
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 the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p.
Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?
Write the formula for the area of the triangle having its vertices at (x1, y1), (x2, y2) and (x3, y3).
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
The distance of the point (4, 7) from the x-axis is
If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______.
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
Point (–3, 5) lies in the ______.
