Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the point P (-3, k) divide the line AB in the ratio s : 1
Then, by the section formula :
`x = (mx_1 + nx_1) /(m+n) , y= (my_2 +ny_1)/(m+n)`
The coordinates of P are (-3,k).
`-3=(-2s-5)/(s+1) , k =(3s-4)/(s+1)`
⇒-3s-3=-2s-5,k(s+1)=3s-4
⇒-3s+2s=-5+3,k(s+1) = 3s-4
⇒-s=-2,k(s+1)= 3s-4
⇒ s =2,k(s+1)=3s-4
Therefore, the point P divides the line AB in the ratio 2 : 1.
Now, putting the value of s in the equation k(s+1)=3s-4 , we get:
k(2+1)=3(2)-4
⇒ 3k=6-4
⇒ 3k = 2⇒k=`2/3`
Therefore, the value of k`= 2/3`
That is, the coordinates of P are `(-3,2/3)`
APPEARS IN
संबंधित प्रश्न
Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-1,-2) B(1, 0), C (-1, 2), D(-3, 0)
Find the points on the y-axis which is equidistant form the points A(6,5) and B(- 4,3)
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)
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
ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of one its diagonal.
Find the value of a, so that the point ( 3,a ) lies on the line represented by 2x - 3y =5 .
Find the centroid of ΔABC whose vertices are A(2,2) , B (-4,-4) and C (5,-8).
Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.
Points P, Q, R and S divides the line segment joining A(1, 2) and B(6, 7) in 5 equal parts. Find the coordinates of the points P, Q and R.
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.
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 .
The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is
The coordinates of the circumcentre of the triangle formed by the points O (0, 0), A (a, 0 and B (0, b) are
If the centroid of the triangle formed by the points (3, −5), (−7, 4), (10, −k) is at the point (k −1), then k =
The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be
A point both of whose coordinates are negative will lie in ______.
Find the coordinates of the point whose ordinate is – 4 and which lies on y-axis.
