Advertisements
Advertisements
प्रश्न
Find the ratio in which the line segment joining A (1, −5) and B (−4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.
उत्तर
Let the ratio in which the line segment joining A (1, −5) and B (−4, 5) is divided by x-axis be K : 1
Therefore, the coordinates of the point of division is
x = `(m_1x_2 + m_2x_1)/(m_1 + m_2), 0 = (m_1y_2 + m_2y_1)/(m_1 + m_2)`
x = `(k (-4) + 1 (1))/(k + 1), 0 = (k (5)+ 1 (-5))/(k + 1)`
x = `(-4k+1)/(k+1), 0 = (5k-5)/(k+1)`
x (k + 1) = -4 + 1 and 5k - 5 = 0
k = 1 Now, x (k + 1) = -4 + 1
⇒ x (1 + 1) = -4 + 1
⇒ 2x = -3
⇒ x = `-3/2`
∴ The required ratio is k:1 = 1:1
Coordinates of P are (x, 0) = `(-3/2,0)`
APPEARS IN
संबंधित प्रश्न
Prove that the points (–2, –1), (1, 0), (4, 3) and (1, 2) are the vertices of a parallelogram. Is it a rectangle ?
If A (5, –1), B(–3, –2) and C(–1, 8) are the vertices of triangle ABC, find the length of median through A and the coordinates of the centroid.
Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, -3) and B is (1, 4).
If two vertices of a parallelogram are (3, 2) (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.
If the points (-2, -1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.
The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively. Find the values of p and q.
P is a point on the line joining A(4, 3) and B(–2, 6) such that 5AP = 2BP. Find the co-ordinates of P.
Find the co-ordinates of the points of tri-section of the line joining the points (–3, 0) and (6, 6).
A (2, 5), B (–1, 2) and C (5, 8) are the co-ordinates of the vertices of the triangle ABC. Points P and Q lie on AB and AC respectively, such that : AP : PB = AQ : QC = 1 : 2.
- Calculate the co-ordinates of P and Q.
- Show that : `PQ = 1/3 BC`.
In what ratio is the line joining A(0, 3) and B(4, –1) divided by the x-axis? Write the co-ordinates of the point where AB intersects the x-axis.
The mid-point of the segment AB, as shown in diagram, is C(4, –3). Write down the co-ordinates of A and B.
Find the coordinate of a point P which divides the line segment joining :
A (3, -3) and B (6, 9) in the ratio 1 :2.
Find the coordinates of point P which divides line segment joining A ( 3, -10) and B (3, 2) in such a way that PB: AB= 1.5.
Find the ratio in which the line y = -1 divides the line segment joining (6, 5) and (-2, -11). Find the coordinates of the point of intersection.
Q is a point on the line segment AB. The coordinates of A and B are (2, 7) and (7, 12) along the line AB so that AQ = 4BQ. Find the coordinates of Q.
Find the ratio in which the line segment joining A (2, -3) and B(S, 6) i~ divided by the x-axis.
In what ratio is the line joining (2, -1) and (-5, 6) divided by the y axis ?
The fourth vertex D of a parallelogram ABCD, whose three vertices are A(–2, 3), B(6, 7) and C(8, 3), is ______.
What is the ratio in which the line segment joining (2, -3) and (5, 6) is divided by x-axis?
