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
On which axis do the following points lie?
S(0,5)
Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
Prove that the points A(-4,-1), B(-2, 4), C(4, 0) and D(2, 3) are the vertices of a rectangle.
Points P, Q, and R in that order are dividing line segment joining A (1,6) and B(5, -2) in four equal parts. Find the coordinates of P, Q and R.
ABCD is rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P,Q,R and S be the midpoints of AB, BC, CD and DA respectively, Show that PQRS is a rhombus.
If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k.
The distance of the point P (4, 3) from the origin is
If three points (x1, y1) (x2, y2), (x3, y3) lie on the same line, prove that \[\frac{y_2 - y_3}{x_2 x_3} + \frac{y_3 - y_1}{x_3 x_1} + \frac{y_1 - y_2}{x_1 x_2} = 0\]
\[A\left( 6, 1 \right) , B(8, 2) \text{ and } C(9, 4)\] are three vertices of a parallelogram ABCD . If E is the mid-point of DC , find the area of \[∆\] ADE.
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
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 the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
The distance of the point (4, 7) from the y-axis is
The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.
The point at which the two coordinate axes meet is called the ______.
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
In which quadrant, does the abscissa, and ordinate of a point have the same sign?
Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x-axis is 1:2.
Reason (R): as formula for the internal division is `((mx_2 + nx_1)/(m + n) , (my_2 + ny_1)/(m + n))`
