Advertisements
Advertisements
प्रश्न
Find the ratio in which the y-axis divides the line segment joining the points (−4, − 6) and (10, 12). Also find the coordinates of the point of division ?
उत्तर
Let the y-axis divide the line segment joining the points (−4, −6) and (10, 12) in the ratio λ : 1. and the point of the intersection be (0, y).
So, by section formula, we have:
`((10lambda+(-4))/(lambda+1),(12lambda+(-6))/(lambda+1))=(0,y)`
`therefore(10lambda+(-4))/(lambda+1)=0rArr10lambda-4=0`
`rArrlambda=4/10=2/5`
`thereforey=(12lambda+(-6))/(lambda+1)=(12xx2/5-6)/(2/5+1)=((24-30/5))/((2+5)/5)`
Thus, the y-axis divides the line segment joining the given points in the ratio 2 : 5 and the point of division is`(0,-6/7)`
APPEARS IN
संबंधित प्रश्न
Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4)
If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.
Show that the mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10).
The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively. Find the values of p and q.
The line joining P(–4, 5) and Q(3, 2) intersects the y-axis at point R. PM and QN are perpendicular from P and Q on the x-axis Find:
- the ratio PR : RQ
- the coordinates of R.
- the area of the quadrilateral PMNQ.
If the point C (–1, 2) 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 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:
Find the ratio in which Y-axis divides the point A(3, 5) and point B(– 6, 7). Find the coordinates of the point
If `P(a/3, 4)` is the mid-point of the line segment joining the points Q(– 6, 5) and R(– 2, 3), then the value of a is ______.
Point C divides the line segment whose points are A(4, –6) and B(5, 9) in the ratio 2:1. Find the coordinates of C.
