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प्रश्न
Calculate the ratio in which the line joining A(6, 5) and B(4, –3) is divided by the line y = 2.
उत्तर
The co-ordinates of every point on the line y = 2 will be of the type (x, 2).
Using section formula, we have:
`y = (m_1 xx (-3) + m_2 xx 5)/(m_1 + m_2)`
`2 = (-3m_1 + 5m_2)/(m_1 + m_2)`
`2m_1 + 2m_2 = -3m_1 + 5m_2`
`2m_1 + 3m_1 = 5m_2 - 2m_2`
`5m_1 = 3m_2`
`m_1/m_2 = 3/5`
Thus, the required ratio is 3 : 5.
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संबंधित प्रश्न
If the points A (6, 1), B (8, 2), C(9, 4) and D(p, 3) are vertices of a parallelogram, taken in order, find the value of p
Find the coordinates of the centroid of a triangle whose vertices are (–1, 0), (5, –2) and (8, 2)
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.
Show that A (3, –2) is a point of trisection of the line segment joining the points (2, 1) and (5, −8). Also, find the co-ordinates of the other point of trisection.
A line segment joining A`(-1,5/3)` and B(a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects the y-axis.
- Calculate the value of ‘a’.
- Calculate the co-ordinates of ‘P’.
Find the ratio in which Y-axis divides the point A(3, 5) and point B(– 6, 7). Find the coordinates of the point
The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
Find the ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1). Also find the coordinates of the point of division.
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.
