Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let the point `P (1/2,y)` divides the line segment joining the points A(3, –5) and B(–7, 9) in the ratio k : 1. Then
` (1/2, y ) = ((k(-7)+3)/(k+1), (k(9)-3)/(k+1))`
`⇒ (-7k +3)/(k+1) = 1/2 and (9k-5)/(k+1) = y `
`⇒ k+1 = - 14k +6`
`⇒ k= 1/3`
`"Now, substituting " k = 1/3 "in" (9k-5)/(k+1) = y `, we get
`(9/3-5)/(1/3+1) = y`
`⇒ y = (9-15)/(1+3)`
`= -3/2`
`"Hence, required ratio is 1 : 3 and "y =-3/2 .`
APPEARS IN
RELATED QUESTIONS
On which axis do the following points lie?
R(−4,0)
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.
If p(x , y) is point equidistant from the points A(6, -1) and B(2,3) A , show that x – y = 3
Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).
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.
In what ratio does the point P(2,5) divide the join of A (8,2) and B(-6, 9)?
Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.
Points (−4, 0) and (7, 0) lie
The area of the triangle formed by the points P (0, 1), Q (0, 5) and R (3, 4) is
In \[∆\] ABC , the coordinates of vertex A are (0, - 1) and D (1,0) and E(0,10) respectively the mid-points of the sides AB and AC . If F is the mid-points of the side BC , find the area of \[∆\] DEF.
Find the value of k, if the points A(7, −2), B (5, 1) and C (3, 2k) are collinear.
If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c.
What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4)?
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is
The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
f the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are
Which of the points P(-1, 1), Q(3, - 4), R(1, -1), S (-2, -3), T(-4, 4) lie in the fourth quadrant?
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
Co-ordinates of origin are ______.
