Advertisements
Advertisements
प्रश्न
The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.
उत्तर
We have given that R divides the line segment AB
AR+ RB = AB
`3/4`AB + RB = AB
⇒ RB = `"AB"/4`
⇒ AR : RB = 3 : 1
Using section formula:
`x = ((m_1x_2 + m_2x_1)/( m_1 + m_2)), y = ((m_1y_2 + m_2y_1)/(m_1 + m_2))`
m1 = 3, m2 = 1
x1 = - 4, y1 = 0
x2 = 0, y2 = 6
Plugging values in the formula we get
x = `( 3 xx 0 + 1 xx (- 4))/( 3 + 1), y = ( 3 xx 6 + 1 xx 0)/( 3 + 1)`
x = `(- 4)/4, y = 18/4`
⇒ x = - 1, y = `9/2`
Therefore, the coordinates of R `(-1,9/2)`
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).
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.
If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides
On which axis do the following points lie?
P(5, 0)
Which point on the x-axis is equidistant from (5, 9) and (−4, 6)?
Prove that the points (−2, 5), (0, 1) and (2, −3) are collinear.
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
Prove that the points A(-4,-1), B(-2, 4), C(4, 0) and D(2, 3) are the vertices of a rectangle.
Show that the points A (1, 0), B (5, 3), C (2, 7) and D (−2, 4) are the vertices of a parallelogram.
Find the co-ordinates of the point which divides the join of A(-5, 11) and B(4,-7) in the ratio 7 : 2
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.
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, -3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
Show that the points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?
If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.
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.
Find the value of a so that the point (3, a) lies on the line represented by 2x − 3y + 5 = 0
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =
