Advertisements
Advertisements
Question
If point P divides segment AB in the ratio 1 : 3 where A(– 5, 3) and B(3, – 5), then the coordinates of P are ______
Options
(– 2, – 2)
(– 1, – 1)
(– 3, 1)
(1, – 3)
Solution
(– 3, 1)
Let A(x1, y1) = A(-5, 3) and B(x2, y2) = B(3, -5),
a : b = 1 : 3
∴ x1 = -5, y1 = 3, x2 = 3, y2 = –5, a = 1, b = 3.
∴ By section formula,
|
∴ x = `(ax_2 + bx_1)/(a + b)` ∴ x = `(1(3) + 3(-5))/(1 + 3)` ∴ x = `(3 - 15)/(4)` ∴ x = `(- 12)/(4)` ∴ x = -3 |
∴ y = `(ay_2 + by_1)/(a + b)` ∴ y = `(1(-5) + 3(3))/(1 + 3)` ∴ y = `(-5 + 9)/(4)` ∴ y = `(4)/(4)` ∴ y = 1 |
∴ Co-ordinates of P are (-3, 1).
APPEARS IN
RELATED QUESTIONS
Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7)
If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Find the ratio in which the join of (–4, 7) and (3, 0) is divided by the y-axis. Also, find the co-ordinates of the point of intersection.
The three vertices of a parallelogram ABCD are A(3, −4), B(−1, −3) and C(−6, 2). Find the coordinates of vertex D and find the area of ABCD.
Find the coordinate of a point P which divides the line segment joining :
M( -4, -5) and N (3, 2) in the ratio 2 : 5.
Find the coordinate of a point P which divides the line segment joining :
A(-8, -5) and B (7, 10) in the ratio 2:3.
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.
Find the points of trisection of the segment joining A ( -3, 7) and B (3, -2).
Show that the lines x = O and y = O trisect the line segment formed by joining the points (-10, -4) and (5, 8). Find the points of trisection.
Find the ratio in which the line segment joining P ( 4, -6) and Q ( -3, 8) is divided by the line y = 0.
Point P(5, –3) is one of the two points of trisection of the line segment joining the points A(7, –2) and B(1, –5).
In what ratio does the x-axis divide the line segment joining the points (– 4, – 6) and (–1, 7)? Find the coordinates of the point of division.
If P(9a – 2, – b) divides line segment joining A(3a + 1, –3) and B(8a, 5) in the ratio 3 : 1, find the values of a and b.
Find the coordinates of the point R on the line segment joining the points P(–1, 3) and Q(2, 5) such that PR = `3/5` PQ.
The points A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC. Find the coordinates of the point P on AD such that AP : PD = 2 : 1
Find the ratio in which the x-axis divides internally the line joining points A (6, -4) and B ( -3, 8).
Complete the following activity to find the coordinates of point P which divides seg AB in the ratio 3:1 where A(4, – 3) and B(8, 5).
Activity:
∴ By section formula,
∴ x = `("m"x_2 + "n"x_1)/square`,
∴ x = `(3 xx 8 + 1 xx 4)/(3 + 1)`,
= `(square + 4)/4`,
∴ x = `square`,
∴ y = `square/("m" + "n")`
∴ y = `(3 xx 5 + 1 xx (-3))/(3 + 1)`
= `(square - 3)/4`
∴ y = `square`
Point C divides the line segment whose points are A(4, –6) and B(5, 9) in the ratio 2:1. Find the coordinates of C.
If (2, 4) is the mid-point of the line segment joining (6, 3) and (a, 5), then the value of a is ______.
Find the co-ordinates of the points of trisection of the line segment joining the points (5, 3) and (4, 5).
