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प्रश्न
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.
उत्तर
Given points are A(4, –6) and B(5, 9) and the ratio is 2:1.
Let the coordinates of C be (x, y).
Then, by the section formula,
x = `(mx_2 + nx_1)/(m + n)`
= `(2 xx 5 + 1 xx 4)/(2 + 1)`
= `(10 + 4)/3`
= `14/3`
y = `(my_2 + ny_1)/(m + n)`
= `(2 xx 9 + 1 xx (-6))/(2 + 1)`
= `(18 - 6)/3`
= `12/3`
= 4
As a result, the coordinates of point C are `(14/3, 4)`.
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संबंधित प्रश्न
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Find the lengths of the medians of a ∆ABC whose vertices are A(7, –3), B(5,3) and C(3,–1)
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).
Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.
If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.
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.
In what ratio does the point (a, 6) divide the join of (–4, 3) and (2, 8)? Also, find the value of a.
In what ratio is the join of (4, 3) and (2, –6) divided by the x-axis? Also, find the co-ordinates of the point of intersection.
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.
If the point C (–1, 2) divides internally the line-segment joining the points A (2, 5) and B (x, y) in the ratio 3 : 4, find the value of x2 + y2 ?
Find the coordinates of a point P, which lies on the line segment joining the points A (−2, −2), and B (2, −4), such that `AP=3/7 AB`.
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.
The points A, B and C divides the line segment MN in four equal parts. The coordinates of Mand N are (-1, 10) and (7, -2) respectively. Find the coordinates of A, B and C.
Find the ratio in which the line segment joining P ( 4, -6) and Q ( -3, 8) is divided by the line y = 0.
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`
If the points A(2, 3), B(–5, 6), C(6, 7) and D(p, 4) are the vertices of a parallelogram ABCD, find the value of p.
If A and B are (– 2, – 2) and (2, – 4) respectively; then find the co-ordinates of the point P such that `(AB)/(AB) = 3/7`.
