Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
The line segment joining the points A(3, -3) and B(-2,7) is divided by x-axis. Let the required ratio be k : 1 So ,
` 0= (k (7) -3)/(k+1) ⇒ k =3/7`
Now,
`"Point of division" = ((k(-2)+3)/(k+1 \) , (k(7)-3)/(k+1))`
`=((3/7 xx(-2)+3)/(3/7+1) , (3/7xx (7) -3)/(3/7 +1)) (∵ k = 3/7)`
`= ((-6+21)/(3+7), (21-21)/(3+7))`
`=(3/2,0)`
`"Hence, the required ratio is 3:7and the point of division is"(3/2, 0)`
APPEARS IN
संबंधित प्रश्न
In Fig. 14.36, a right triangle BOA is given C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A and B.
We have a right angled triangle,`triangle BOA` right angled at O. Co-ordinates are B (0,2b); A (2a, 0) and C (0, 0).
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.
Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.
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.
If the point ( x,y ) is equidistant form the points ( a+b,b-a ) and (a-b ,a+b ) , prove that bx = ay
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?
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 points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p.
If (x, y) be on the line joining the two points (1, −3) and (−4, 2) , prove that x + y + 2= 0.
If \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and } F\left( \frac{7}{2}, \frac{7}{2} \right)\] are the mid-points of sides of \[∆ ABC\] , find the area of \[∆ ABC\] .
Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).
If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
The ratio in which the line segment joining P (x1, y1) and Q (x2, y2) is divided by x-axis is
If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______
The coordinates of two points are P(4, 5) and Q(–1, 6). Find the difference between their abscissas.
Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1
Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.
