Advertisements
Advertisements
Question
Find the co-ordinates of the point which divides the join of A(-5, 11) and B(4,-7) in the ratio 7 : 2
Advertisements
Solution
The end points of AB are A(-5, 11) and B(4,-7)
Therefore `(x_1=-5, y
_1=11) and (x_2 = 4, y_2 = -7)`
Also, m = 7 and n= 2
Let the required point be p(x,y) .
By section formula, we get
`x = ((mx_2 +nx_1))/((m+n)) , y= ((my_2+ny_1))/((m+n))`
`⇒ x = ({ 7 xx 4 + 2 xx (-5)})/(7 +2) , y = ({ 7xx (-7) + 2 xx11})/(7 +2)` `⇒ x = (28-10)/9 , y = (-49 +22)/9`
`⇒ x = 18/9 , y = -27/9 `
Therefore , x = 2 and y = -3
Hence, the required point are P =(2,-3).
APPEARS IN
RELATED QUESTIONS
On which axis do the following points lie?
P(5, 0)
Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and(1, 2) meet
If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.
If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
Find the points on the y-axis which is equidistant form the points A(6,5) and B(- 4,3)
The midpoint of the line segment joining A (2a, 4) and B (-2, 3b) is C (1, 2a+1). Find the values of a and b.
In what ratio is the line segment joining the points A(-2, -3) and B(3,7) divided by the yaxis? Also, find the coordinates of the point of division.
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
If the point P(k - 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the value of k.
If `P(a/2,4)`is the mid-point of the line-segment joining the points A (−6, 5) and B(−2, 3), then the value of a is
If the centroid of the triangle formed by points P (a, b), Q(b, c) and R (c, a) is at the origin, what is the value of a + b + c?
Write the coordinates the reflections of points (3, 5) in X and Y -axes.
The distance between the points (cos θ, 0) and (sin θ − cos θ) is
f 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 point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).
If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______
Find the coordinates of the point of intersection of the graph of the equation x = 2 and y = – 3
Find the coordinates of the point whose ordinate is – 4 and which lies on y-axis.
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So, he started to sketch his own rocket designs on the graph sheet. One such design is given below :
Based on the above, answer the following questions:
i. Find the mid-point of the segment joining F and G. (1)
ii. a. What is the distance between the points A and C? (2)
OR
b. Find the coordinates of the points which divides the line segment joining the points A and B in the ratio 1 : 3 internally. (2)
iii. What are the coordinates of the point D? (1)
