Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7) - Mathematics

Advertisements
Advertisements
Sum

Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7)

Advertisements

Solution

Suppose the line 3x + y – 9 = 0 divides the line segment joining A (1, 3) and B(2, 7) in the ratio k : 1 at point C. Then, the coordinates of C are

`( \frac{2k+1}{k+1},\ \frac{7k+3}{k+1})`

But, C lies on 3x + y – 9 = 0. Therefore,

`3( \frac{2k+1}{k+1})+\frac{7k+3}{k+1}-9=0`

⇒ 6k + 3 + 7k + 3 – 9k – 9 = 0

`⇒ k = \frac { 3 }{ 4 }`

So, the required ratio is 3 : 4 internally

Type III : On determination of the type of a given quadrilateral

Concept: Section Formula
  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

If the coordinates of the mid-points of the sides of a triangle are (1, 2) (0, –1) and (2, 1). Find the coordinates of its vertices.


If A and B are (− 2, − 2) and (2, − 4), respectively, find the coordinates of P such that `AP = 3/7 AB` and P lies on the line segment AB.


If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.


The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively. Find the values of p and q.


The point P (5, -4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the co-ordinates of points A and B.


The line segment joining A (2, 3) and B (6, -5) is intercepted by x-axis at the point K. Write down the ordinate of the point K. Hence, find the ratio in which K divides AB. Also find the coordinates of the point K.


Find the co-ordinates of the centroid of a triangle ABC whose vertices are: A(-1, 3), B(1, -1) and C(5, 1)


The mid point of the line segment joining (4a, 2b -3) and (-4, 3b) is (2, -2a). Find the values of a and b.


If the point C (–1, 2) divides internally the line-segment joining the points A (2, 5) and B (xy) in the ratio 3 : 4, find the value of x2 + y2 ?


Find the length of the hypotenuse of a square whose side is 16 cm.


Find the coordinate of a point P which divides the line segment joining :

D(-7, 9) and E( 15, -2) in the ratio 4:7. 


Find the ratio in which the line x = -2 divides the line segment joining (-6, -1) and (1, 6). Find the coordinates of the point of intersection. 


The line joining P (-5, 6) and Q (3, 2) intersects the y-axis at R. PM and QN are perpendiculars from P and Q on the x-axis. Find the ratio PR: RQ. 


A (2, 5), B (-1, 2) and C (5, 8) are the vertices of triangle ABC. Point P and Q lie on AB and AC respectively, such that AP: PB = AQ: QC = 1: 2. Calculate the coordinates of P and Q. Also, show that 3PQ = BC. 


In what ratio is the line joining (2, -1) and (-5, 6) divided by the y axis ?


In the figure given below, the line segment AB meets X-axis at A and Y-axis at B. The point P (- 3, 4) on AB divides it in the ratio 2 : 3. Find the coordinates of A and B.


Using section formula, show that the points A(7, −5), B(9, −3) and C(13, 1) are collinear


If point P(1, 1) divide segment joining point A and point B(–1, –1) in the ratio 5 : 2, then the coordinates of A are ______


If point P divides segment AB in the ratio 1 : 3 where A(– 5, 3) and B(3, – 5), then the coordinates of P are ______


The point Q divides segment joining A(3, 5) and B(7, 9) in the ratio 2 : 3. Find the X-coordinate of Q


Point P(– 4, 6) divides point A(– 6, 10) and B(m, n) in the ratio 2:1, then find the coordinates of point B


Find the ratio in which Y-axis divides the point A(3, 5) and point B(– 6, 7). Find the coordinates of the point


If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of ‘a’ is ______.


Find the coordinates of the point R on the line segment joining the points P(–1, 3) and Q(2, 5) such that PR = `3/5` PQ.


If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.


Complete the following activity to find the coordinates of point P which divides seg AB in the ratio 3:1 where A(4, – 3) and B(8, 5).

Activity:

∴ By section formula,

∴ x = `("m"x_2 + "n"x_1)/square`, 

∴ x = `(3 xx 8 + 1 xx 4)/(3 + 1)`,

= `(square + 4)/4`,

∴ x = `square`,

∴ y = `square/("m" + "n")`

∴ y = `(3 xx 5 + 1 xx (-3))/(3 + 1)`

= `(square - 3)/4`

∴ y = `square`


Point C divides the line segment whose points are A(4, –6) and B(5, 9) in the ratio 2:1. Find the coordinates of C.


In what ratio does the Y-axis divide the line segment P(– 3, 1) and Q(6, 2)?


Find the ratio in which the line segment joining the points A(6, 3) and B(–2, –5) is divided by x-axis.


Find the co-ordinates of the points of trisection of the line segment joining the points (5, 3) and (4, 5).


Share
Notifications



      Forgot password?
Use app×