Advertisements
Advertisements
प्रश्न
In what ratio does the point C (4,5) divides the join of A (2,3) and B (7,8) ?
Advertisements
उत्तर
Let the required ratio be k : 1
Then, by section formula, the coordinates of C are
`c((7k+2)/(k+1) , (8k+3)/(k+1))`
Therefore,
`(7k+2)/(k+1) =4 and (8k+3)/(k+1) =5 [∵C (4,5) is given]`
`⇒7k + 2 =4k + 4 and 8k +3=5k +5 ⇒ 3k =2`
`⇒ k = 2/3`in each case
So, the required ratio is `2/3 `: 1 , which is same as 2 : 3.
APPEARS IN
संबंधित प्रश्न
If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides
Find the points of trisection of the line segment joining the points:
(3, -2) and (-3, -4)
Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
Find the coordinates of the midpoints of the line segment joining
P(-11,-8) and Q(8,-2)
Find the ratio in which the pint (-3, k) divide the join of A(-5, -4) and B(-2, 3),Also, find the value of k.
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
Find the value of k, if the points A (8, 1) B(3, −4) and C(2, k) are collinear.
What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4)?
Write the coordinates of a point on X-axis which is equidistant from the points (−3, 4) and (2, 5).
Write the formula for the area of the triangle having its vertices at (x1, y1), (x2, y2) and (x3, y3).
Find the value of a so that the point (3, a) lies on the line represented by 2x − 3y + 5 = 0
If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y.
Find the coordinates of the point which is equidistant from the three vertices A (\[2x, 0) O (0, 0) \text{ and } B(0, 2y) of ∆\] AOB .
If A (2, 2), B (−4, −4) and C (5, −8) are the vertices of a triangle, than the length of the median through vertex C is
If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =
If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______.
What are the coordinates of origin?
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.
