Advertisements
Advertisements
प्रश्न
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
पर्याय
−2 : 3
−3 : 2
3 : 2
2 : 3
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 + n ) , (my_2 + n y_1)/(m + n ))`
Here it is said that the point (4, 5) divides the points A(2,3) and B(7,8). Substituting these values in the above formula we have,
`(4,5) = ((m(7)+n(2))/(m+n) , (m(8)+n(3))/(m+n))`
Equating the individual components we have,
`4 = ((m (7) + n(2) )/(m+n)) `
`4m + 4n = 7m + 2 n`
`3m = 2n `
`m/n = 2/3`
APPEARS IN
संबंधित प्रश्न
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.
Find the distance between the following pair of points:
(a, 0) and (0, b)
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
Find the point on x-axis which is equidistant from the points (−2, 5) and (2,−3).
Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1), (1, 3) and (x, 8) respectively.
Show that the points A(3,0), B(4,5), C(-1,4) and D(-2,-1) are the vertices of a rhombus. Find its area.
Find the coordinates of the midpoints of the line segment joining
P(-11,-8) and Q(8,-2)
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
Find the ratio which the line segment joining the pints A(3, -3) and B(-2,7) is divided by x -axis Also, find the point of division.
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.
Find the coordinates of the circumcentre of a triangle whose vertices are (–3, 1), (0, –2) and (1, 3).
The abscissa of any point on y-axis is
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k
The coordinates of the circumcentre of the triangle formed by the points O (0, 0), A (a, 0 and B (0, b) are
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
Point (–10, 0) lies ______.
If y-coordinate of a point is zero, then this point always lies ______.
The points whose abscissa and ordinate have different signs will lie in ______.
