Advertisements
Advertisements
प्रश्न
The ratio in which the line segment joining points A (a1, b1) and B (a2, b2) is divided by y-axis is
पर्याय
−a1 : a2
a1 : a2
b1 : b2
−b1 : b2
उत्तर
Let P( 0 ,y) be the point of intersection of y-axis with the line segment joining` A(a_1 , b_1) " and B " (a_2 , b_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,
`( 0, y) = ((λa_2 +a_1)/(λ + 1) , ( λb_2 + b_1) /(λ + 1))`
Now equate the x component on both the sides,
`(λa_2 + a_1) /(λ + 1) = 0`
On further simplification,
`λ = - a_1/a_2`
APPEARS IN
संबंधित प्रश्न
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when The centre of the square is at the origin and coordinate axes are parallel to the sides AB and AD respectively.
Which point on the y-axis is equidistant from (2, 3) and (−4, 1)?
Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
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 point A (4,3) and B ( x,5) lies on a circle with the centre o (2,3) . Find the value of x.
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.
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
If the point \[C \left( - 1, 2 \right)\] divides internally the line segment joining the points A (2, 5) and B( x, y ) in the ratio 3 : 4 , find the value of x2 + y2 .
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 perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?
Find the value of a so that the point (3, a) lies on the line represented by 2x − 3y + 5 = 0
If (−1, 2), (2, −1) and (3, 1) are any three vertices of a parallelogram, then
f the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are
The points (–5, 2) and (2, –5) lie in the ______.
If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has ______.
The point whose ordinate is 4 and which lies on y-axis is ______.
Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
