Advertisements
Advertisements
प्रश्न
In what ratio is the line segment joining the points A(-2, -3) and B(3,7) divided by the yaxis? Also, find the coordinates of the point of division.
उत्तर
Let AB be divided by the x-axis in the ratio :1 k at the point P.
Then, by section formula the coordination of P are
`p = ((3k-2)/(k+1) , (7k-3)/(k+1))`
But P lies on the y-axis; so, its abscissa is 0.
Therefore , `(3k-2)/(k+1) = 0`
`⇒ 3k-2 = 0 ⇒3k=2 ⇒ k = 2/3 ⇒ k = 2/3 `
Therefore, the required ratio is `2/3:1`which is same as 2 : 3
Thus, the x-axis divides the line AB in the ratio 2 : 3 at the point P.
Applying `k= 2/3,` we get the coordinates of point.
`p (0,(7k-3)/(k+1))`
`= p(0, (7xx2/3-3)/(2/3+1))`
`= p(0, ((14-9)/3)/((2+3)/3))`
`= p (0,5/5)`
= p(0,1)
Hence, the point of intersection of AB and the x-axis is P (0,1).
APPEARS IN
संबंधित प्रश्न
On which axis do the following points lie?
P(5, 0)
Find the coordinates of the point which divides the line segment joining (−1,3) and (4, −7) internally in the ratio 3 : 4
In what ratio is the line segment joining the points (-2,-3) and (3, 7) divided by the y-axis? Also, find the coordinates of the point of division.
If the poin A(0,2) is equidistant form the points B (3, p) and C (p ,5) find the value of p. Also, find the length of AB.
If the point A (4,3) and B ( x,5) lies on a circle with the centre o (2,3) . Find the value of x.
Show that the following points are the vertices of a square:
(i) A (3,2), B(0,5), C(-3,2) and D(0,-1)
Points P, Q, and R in that order are dividing line segment joining A (1,6) and B(5, -2) in four equal parts. Find the coordinates of P, Q and R.
In what ratio is the line segment joining A(2, -3) and B(5, 6) divide by the x-axis? Also, find the coordinates of the pint of division.
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
A point whose abscissa and ordinate are 2 and −5 respectively, lies in
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.
If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 + b3 + c3 =
If points A (5, p) B (1, 5), C (2, 1) and D (6, 2) form a square ABCD, then p =
If A(x, 2), B(−3, −4) and C(7, −5) are collinear, then the value of x is
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
Point (–10, 0) lies ______.
