Advertisements
Advertisements
Question
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.
Solution
The ratio in which the y-axis divides two points `(x_1,y_1)` and (x_2,y_2) is λ : 1
The coordinates of the point dividing two points `(x_1,y_1)` and `(x_2, y_2)` in the ratio m:n is given as,
`(x,y) = (((lambdax_2+ x_1)/(lambda + 1))"," ((lambday_2 + y_1)/(lambda +1)))` where `lambda = m/n`
Here the two given points are A(-2,-3) and B(3,7).
Since the point is on the y-axis so, x coordinate is 0.
`(3lambda - 2)/1 = 0`
`=> lambda = 2/3`
Thus the given points are divided by the y-axis in the ratio 2:3
The coordinates of this point (x, y) can be found by using the earlier mentioned formula.
`(x,y) = (((2/3(3) + (-2))/(2/3 + 1))","((2/3(7) + (-3))/(2/3 + 1)))`
`(x,y) = ((((6 - 2(3))/3)/((2+3)/3)) "," (((14 - 3(3))/3)/((2+3)/3)))`
`(x,y) = ((0/5)","(5/5))`
(x,y) = (0,1)
Thus the co-ordinates of the point which divides the given points in the required ratio are (0,1)
APPEARS IN
RELATED QUESTIONS
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.
On which axis do the following points lie?
Q(0, -2)
Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).
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.
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, -3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.
If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k,5), find the value of k.
The abscissa and ordinate of the origin are
The measure of the angle between the coordinate axes is
A point whose abscissa and ordinate are 2 and −5 respectively, lies in
If (a,b) is the mid-point of the line segment joining the points A (10, - 6) , B (k,4) and a - 2b = 18 , find the value of k and the distance AB.
If the point \[C \left( - 1, 2 \right)\] divides internally the line segment joining the points A (2, 5) and B( x, y ) in the ratio 3 : 4 , find the value of x2 + y2 .
If (x, y) be on the line joining the two points (1, −3) and (−4, 2) , prove that x + y + 2= 0.
If the distance between the points (3, 0) and (0, y) is 5 units and y is positive. then what is the value of y?
If the distance between the points (4, p) and (1, 0) is 5, then p =
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
The coordinates of the circumcentre of the triangle formed by the points O (0, 0), A (a, 0 and B (0, b) are
The line segment joining the points A(2, 1) and B (5, - 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x - y + k= 0 find the value of k.
Find the coordinates of point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4).
Co-ordinates of origin are ______.
The coordinates of the point where the line 2y = 4x + 5 crosses x-axis is ______.
