Advertisements
Advertisements
प्रश्न
In what ratio does the point P(2,5) divide the join of A (8,2) and B(-6, 9)?
उत्तर
Let the point P (2,5) divide AB in the ratio k : 1
Then, by section formula, the coordinates of P are
` x= (-6k+8)/(k+1) , y = (9k+2)/(k+1)`
It is given that the coordinates of P are ( 2,5).
`⇒ 2= (-6k +8) /(k+1) , 5 =(9k +2) /(k+1) `
⇒ 2k + 2 = -6k +8 , 5k +5 = 9k +2
⇒ 2k + 6k = 8 -2 , 5-2=9k-5k
⇒ 8k = 6, 4k =3
⇒` k = 6/8, k = 3/4 `
`⇒ k = 3/4 ` in each case..
Therefore, the point P (2,5) divides AB in the ratio3:4
APPEARS IN
संबंधित प्रश्न
How will you describe the position of a table lamp on your study table to another person?
(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).
Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.
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 on the y-axis which is equidistant form the points A(6,5) and B(- 4,3)
The line segment joining the points A(3,−4) and B(1,2) is trisected at the points P(p,−2) and Q `(5/3,q)`. Find the values of p and q.
The base QR of a n equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.
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.
If the points A (2,3), B (4,k ) and C (6,-3) are collinear, find the value of k.
Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5, 6), B(1, –2) and C(3, –2).
If the point P(x, 3) is equidistant from the point A(7, −1) and B(6, 8), then find the value of x and find the distance AP.
Find the coordinates of the point which is equidistant from the three vertices A (\[2x, 0) O (0, 0) \text{ and } B(0, 2y) of ∆\] AOB .
If the distance between the points (4, p) and (1, 0) is 5, then p =
If the points(x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =
The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (−3, 4) are
The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be
Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).
A point both of whose coordinates are negative will lie in ______.
