Advertisements
Advertisements
Question
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.
Solution
Let the point P (-3, k) divide the line AB in the ratio s : 1
Then, by the section formula :
`x = (mx_1 + nx_1) /(m+n) , y= (my_2 +ny_1)/(m+n)`
The coordinates of P are (-3,k).
`-3=(-2s-5)/(s+1) , k =(3s-4)/(s+1)`
⇒-3s-3=-2s-5,k(s+1)=3s-4
⇒-3s+2s=-5+3,k(s+1) = 3s-4
⇒-s=-2,k(s+1)= 3s-4
⇒ s =2,k(s+1)=3s-4
Therefore, the point P divides the line AB in the ratio 2 : 1.
Now, putting the value of s in the equation k(s+1)=3s-4 , we get:
k(2+1)=3(2)-4
⇒ 3k=6-4
⇒ 3k = 2⇒k=`2/3`
Therefore, the value of k`= 2/3`
That is, the coordinates of P are `(-3,2/3)`
APPEARS IN
RELATED QUESTIONS
The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.
Find the ratio in which the point (-1, y) lying on the line segment joining points A(-3, 10) and (6, -8) divides it. Also, find the value of y.
If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k.
Show that the points (−2, 3), (8, 3) and (6, 7) are the vertices of a right triangle ?
Find the ratio in which the line segment joining the points A(3, 8) and B(–9, 3) is divided by the Y– axis.
The abscissa and ordinate of the origin are
The measure of the angle between the coordinate axes is
If P ( 9a -2 , - b) divides the line segment joining A (3a + 1 , - 3 ) and B (8a, 5) in the ratio 3 : 1 , find the values of a and b .
Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.
If three points (x1, y1) (x2, y2), (x3, y3) lie on the same line, prove that \[\frac{y_2 - y_3}{x_2 x_3} + \frac{y_3 - y_1}{x_3 x_1} + \frac{y_1 - y_2}{x_1 x_2} = 0\]
Find the values of x for which the distance between the point P(2, −3), and Q (x, 5) is 10.
If P (2, 6) is the mid-point of the line segment joining A(6, 5) and B(4, y), find y.
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is
In Fig. 14.46, the area of ΔABC (in square units) is
Find the coordinates of the point which lies on x and y axes both.
