Advertisements
Advertisements
Question
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.
Solution
Let AB be divided by the x-axis in the ratio k : 1 at the point P.
Then, by section formula the coordination of P are
`p = ((5k+2)/(k+1),(6k-3)/(k+1))`
But P lies on the x-axis; so, its ordinate is 0.
Therefore , `(6k-3)/(k+1) = 0`
`⇒ 6k -3=0 ⇒ 6k =3 ⇒k = 3/6 ⇒ k = 1/2`
Therefore, the required ratio is `1/2:1 `, which is same as 1 : 2
Thus, the x-axis divides the line AB li the ratio 1 : 2 at the point P.
Applying `k=1/2` we get the coordinates of point.
`p((5k+1)/(k+1) , 0)`
`=p((5xx1/2+2)/(1/2+1),0)`
`= p (((5+4)/2)/((5+2)/2),0)`
`= p (9/3,0)`
= p (3,0)
Hence, the point of intersection of AB and the x-axis is P( 3,0).
APPEARS IN
RELATED QUESTIONS
On which axis do the following points lie?
Q(0, -2)
Which point on the x-axis is equidistant from (5, 9) and (−4, 6)?
Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3,5).
Determine the ratio in which the point P (m, 6) divides the join of A(-4, 3) and B(2, 8). Also, find the value of m.
Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).
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.
The base QR of a n equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.
Find the area of a quadrilateral ABCD whose vertices area A(3, -1), B(9, -5) C(14, 0) and D(9, 19).
The abscissa and ordinate of the origin are
Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by the x-axis. Also, find the coordinates of the point of division.
If (x, y) be on the line joining the two points (1, −3) and (−4, 2) , prove that x + y + 2= 0.
Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?
Find the distance between the points \[\left( - \frac{8}{5}, 2 \right)\] and \[\left( \frac{2}{5}, 2 \right)\] .
If P (2, 6) is the mid-point of the line segment joining A(6, 5) and B(4, y), find y.
The distance of the point (4, 7) from the y-axis is
If points A (5, p) B (1, 5), C (2, 1) and D (6, 2) form a square ABCD, then p =
If (−2, 1) is the centroid of the triangle having its vertices at (x , 0) (5, −2), (−8, y), then x, y satisfy the relation
If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is
Find the point on the y-axis which is equidistant from the points (S, - 2) and (- 3, 2).
Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.
Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
