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
विकल्प
−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
Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by x-axis Also, find the coordinates of the point of division in each case.
Show that the points A (1, 0), B (5, 3), C (2, 7) and D (−2, 4) are the vertices of a parallelogram.
In what ratio does the point (−4, 6) divide the line segment joining the points A(−6, 10) and B(3,−8)?
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in five equal parts. Find the coordinates of the points P,Q and R
Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
The area of the triangle formed by the points P (0, 1), Q (0, 5) and R (3, 4) is
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.
\[A\left( 6, 1 \right) , B(8, 2) \text{ and } C(9, 4)\] are three vertices of a parallelogram ABCD . If E is the mid-point of DC , find the area of \[∆\] ADE.
If the points A (1,2) , O (0,0) and C (a,b) are collinear , then find a : b.
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=
The point on the x-axis which is equidistant from points (−1, 0) and (5, 0) is
If A(4, 9), B(2, 3) and C(6, 5) are the vertices of ∆ABC, then the length of median through C is
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
The distance of the point (–4, 3) from y-axis is ______.
