Advertisements
Advertisements
प्रश्न
In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?
Advertisements
उत्तर
The co-ordinates of a point which divided two points `(x_1,y_1)` and `(x_2, y_2)` internally in the ratio m:n is given by the formula,
`(x,y) = (((mx_2 + nx_1)/(m + 2))","((my_2 + ny_1)/(m + n)))`
Here it is said that the point `(-5, -21/5)` divides the points (-3,-1) and (-8,-9).
Substituting these values in the above formula we have,
`(-5, -21/5) = (((m(-8) + n(-3))/(m + n))","((m(-9) + n(-1))/(m+ n)))`
Equating the individual components we have,
`-5 = (m(-8) + n(-3))/(m + n)`
-5m - 5n = -8m - 3n
3m = 2n
`m/n = 2/3`
Therefore the ratio in which the line is divided is 2:3
APPEARS IN
संबंधित प्रश्न
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.
On which axis do the following points lie?
R(−4,0)
If (−2, 3), (4, −3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.
Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).
Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.
Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus.
Also, find its area.
Determine the ratio in which the point (-6, a) divides the join of A (-3, 1) and B (-8, 9). Also, find the value of a.
Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).
ΔXYZ ∼ ΔPYR; In ΔXYZ, ∠Y = 60o, XY = 4.5 cm, YZ = 5.1 cm and XYPY =` 4/7` Construct ΔXYZ and ΔPYR.
The area of the triangle formed by the points A(2,0) B(6,0) and C(4,6) is
If (x, y) be on the line joining the two points (1, −3) and (−4, 2) , prove that x + y + 2= 0.
If the point P (m, 3) lies on the line segment joining the points \[A\left( - \frac{2}{5}, 6 \right)\] and B (2, 8), find the value of m.
If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
If the points(x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =
If the points P (x, y) is equidistant from A (5, 1) and B (−1, 5), then
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
A point both of whose coordinates are negative will lie in ______.
Find the coordinates of the point whose abscissa is 5 and which lies on x-axis.
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.
