Advertisements
Advertisements
प्रश्न
Find the ratio in which the point (2, y) divides the line segment joining the points A (-2,2) and B (3, 7). Also, find the value of y.
Advertisements
उत्तर
The co-ordinates of a point which divided two points`(x_1,y_1)` and `(x_2,y_2)` internally in the ratio m:n is given by the formula,
`(x,y) = ((mx_2 + nx_1)/(m + n)), ((my_2 + ny_1)/(m+n)))`
Here we are given that the point P(2,y) divides the line joining the points A(−2,2) and B(3,7) in some ratio.
Let us substitute these values in the earlier mentioned formula.
`(2,y) = (((m(3) +n(-2))/(m + n))"," ((m(7)+n(2))/(m+n)))`
Equating the individual components we have
`2 = (m(3) + n(-2))/(m + n)`
2m + 2n = 3m - 2n
m - 4n
`m/n = 4/1`
We see that the ratio in which the given point divides the line segment is 4: 1.
Let us now use this ratio to find out the value of ‘y’.
`(2,y) = (((m(3) + n(-2))/(m + n))"," ((m(7) + n(2))/(m + n)))`
`(2,y) = (((4(3) + 1(-2))/(4 +1))","((4(7) + 1(2))/(4 +1)))`
Equating the individual components we have
`y = (4(7) + 1()2)/(4 + 1)`
y = 6
Thus the value of ‘y’ is 6
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).
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.
In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at A(3, 1), B(6, 4), and C(8, 6). Do you think they are seated in a line?
Show that the points A (1, 0), B (5, 3), C (2, 7) and D (−2, 4) are the vertices of a parallelogram.
Determine the ratio in which the point (-6, a) divides the join of A (-3, 1) and B (-8, 9). Also, find the value of a.
Show that the following points are the vertices of a square:
A (6,2), B(2,1), C(1,5) and D(5,6)
If the point `P (1/2,y)` lies on the line segment joining the points A(3, –5) and B(–7, 9) then find the ratio in which P divides AB. Also, find the value of y.
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
Prove hat the points A (2, 3) B(−2,2) C(−1,−2), and D(3, −1) are the vertices of a square ABCD.
If points Q and reflections of point P (−3, 4) in X and Y axes respectively, what is QR?
A line intersects the y-axis and x-axis at P and Q , respectively. If (2,-5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
What is the nature of the line which includes the points (-5, 5), (6, 5), (-3, 5), (0, 5)?
In the above figure, seg PA, seg QB and RC are perpendicular to seg AC. From the information given in the figure, prove that: `1/x + 1/y = 1/z`
The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.
The distance of the point P(2, 3) from the x-axis is ______.
Point (–3, 5) lies in the ______.
Signs of the abscissa and ordinate of a point in the second quadrant are respectively.
Point (–10, 0) lies ______.
The distance of the point (–4, 3) from y-axis is ______.
Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate of a point on y-axis is zero.
