Advertisements
Advertisements
प्रश्न
Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by y-axis. Also, find the coordinates of the point of division in each case.
Advertisements
उत्तर
The ratio in which the x−axis divides two points `(x_1,y_1)` and `(x_2,y_2)` is λ : 1
The ratio in which the y-axis divides two points `(x_1,y_1)` and `(x_2,y_2)` is μ : 1
The coordinates of the point dividing two points `(x_1,y_1)` and `(x_2,y_2)` in the ratio m:n is given as,
`(x,y) = (((lambdax_2 + x_1)/(lambda + 1))","((lambday_2 + y_1)/(lambda + 1)))` Where `lambda = m/n`
Here the two given points are A(−2,−3) and B(5,6).
The ratio in which the y-axis divides these points is `(5mu - 2)/3 = 0`
`=> mu= 2/5`
Let point P(x, y) divide the line joining ‘AB’ in the ratio 2: 5
Substituting these values in the earlier mentioned formula we have,
`(x,y) = (((2/5(5) + (-2))/(2/5 + 1))","((2/5(6) + (-3))/(2/5 + 1)))`
`(x,y) = ((((10 + 5(-2))/5)/((2 + 5)/5)) "," (((12 + 5(-3))/3)/((2 + 5)/5)))`
`(x,y) = ((0/7)","(- 3/7))`
`(x,y) = (0, - 3/7)`
Thus the ratio in which the x-axis divides the two given points and the co-ordinates of the point is 2:5 and `(0, - 3/7)`
APPEARS IN
संबंधित प्रश्न
(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
- how many cross - streets can be referred to as (4, 3).
- how many cross - streets can be referred to as (3, 4).
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.
Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).
Find the points of trisection of the line segment joining the points:
5, −6 and (−7, 5),
Find the points of trisection of the line segment joining the points:
(3, -2) and (-3, -4)
If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
If the point ( x,y ) is equidistant form the points ( a+b,b-a ) and (a-b ,a+b ) , prove that bx = ay
Find the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8) Also, find the value of m.
Find the ratio in which the pint (-3, k) divide the join of A(-5, -4) and B(-2, 3),Also, find the value of k.
The abscissa of any point on y-axis 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.
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
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 distance of the point P(2, 3) from the x-axis is ______.
Point (–3, 5) lies in the ______.
Seg AB is parallel to X-axis and coordinates of the point A are (1, 3), then the coordinates of the point B can be ______.
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
In which quadrant, does the abscissa, and ordinate of a point have the same sign?
