Advertisements
Advertisements
Question
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
Options
−2 : 3
−3 : 2
3 : 2
2 : 3
Advertisements
Solution
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
RELATED QUESTIONS
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.
Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
Find the points of trisection of the line segment joining the points:
5, −6 and (−7, 5),
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
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.
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
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.
Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in five equal parts. Find the coordinates of the points P,Q and R
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 area of quadrilateral ABCD whose vertices are A(-3, -1), B(-2,-4) C(4,-1) and D(3,4)
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
Show that A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4) are the vertices of a
rhombus ABCD.
Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
If points (a, 0), (0, b) and (1, 1) are collinear, then \[\frac{1}{a} + \frac{1}{b} =\]
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.
Abscissa of a point is positive in ______.
The distance of the point (–4, 3) from y-axis is ______.
Distance of the point (6, 5) from the y-axis is ______.
