Advertisements
Advertisements
Question
The ratio in which the line segment joining P (x1, y1) and Q (x2, y2) is divided by x-axis is
Options
y1 : y2
−y1 : y2
x1 : x2
−x1 : x2
Solution
Let C( x , 0) be the point of intersection of x-axis with the line segment joining p(x1 , y1) and Q(x2,y2) which divides the line segment PQ 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) = ((λx_2 + x_1)/(λ+1) , (λy_2 + y_1)/(λ + 1))`
Now equate the y component on both the sides,
`(λy_2 + y_1)/(λ + 1) = 0`
On further simplification,
`λ = ( y_1) /(y_2)`
APPEARS IN
RELATED QUESTIONS
Which point on the x-axis is equidistant from (5, 9) and (−4, 6)?
If G be the centroid of a triangle ABC, prove that:
AB2 + BC2 + CA2 = 3 (GA2 + GB2 + GC2)
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 the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and(1, 2) meet
In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?
Show that the points A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram. Is this figure a rectangle?
Find the ratio in which the point (-1, y) lying on the line segment joining points A(-3, 10) and (6, -8) divides it. Also, find the value of y.
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 ratio in which the line segment joining the points A(3, 8) and B(–9, 3) is divided by the Y– axis.
Points (−4, 0) and (7, 0) lie
A point whose abscissa is −3 and ordinate 2 lies in
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 the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.
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.
Write the condition of collinearity of points (x1, y1), (x2, y2) and (x3, y3).
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.
Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.
Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
Distance of the point (6, 5) from the y-axis is ______.
