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प्रश्न
Find the ratio in which the line segment joining P ( 4, -6) and Q ( -3, 8) is divided by the line y = 0.
उत्तर
Given PQ is divided by the line Y = O i.e. x-axis.
Let S (x, O) be the pcint on line Y = 0, which divides the line segment PQ in the ratio k : 1.
Coordinates of S are
x = `(-3"k" + 4)/("k" + 1) , 0 = (8"k" - 6)/("k" + 1)`
⇒ 8 k = 6
⇒ k = `3/4`
Hence, the required ratio is 3: 4.
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संबंधित प्रश्न
If A(–2, –1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram, find the values of a and b
Find the lengths of the medians of a ΔABC having vertices at A(5, 1), B(1, 5), and C(-3, -1).
If the points A (6, 1), B (8, 2), C (9, 4) and D (k, p) are the vertices of a parallelogram taken in order, then find the values of k and p.
Calculate the ratio in which the line joining A(6, 5) and B(4, –3) is divided by the line y = 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 coordinates of the points of trisection of the line segment joining the points (3, -3) and ( 6, 9).
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.
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`
Find the ratio in which the line segment joining the points A(6, 3) and B(–2, –5) is divided by x-axis.
Find the co-ordinates of the points of trisection of the line segment joining the points (5, 3) and (4, 5).
