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प्रश्न
Calculate the ratio in which the line joining the points (–3, –1) and (5, 7) is divided by the line x = 2. Also, find the co-ordinates of the point of intersection.
उत्तर
The co-ordinates of every point on the line x = 2 will be of the type (2, y).
Using section formula, we have:
`x = (m_1 xx 5 + m_2 xx (-3))/(m_1 + m_2)`
`2 = (5m_1 - 3m_2)/(m_1 + m_2)`
`2m_1 + 2m_2 = 5m_1 - 3m_2`
`5m_2 = 3m_1`
`m_1/m_2 = 5/3`
Thus, the required ratio is 5 : 3.
`y = (m_1 xx 7 + m_2 xx (-1))/(m_1 + m_2)`
`y = (5 xx 7 + 3 xx (-1))/(5 + 3)`
`y = (35 - 3)/8`
`y = 32/8`
`y = 4`
Thus, the required co-ordinates of the point of intersection are (2, 4).
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संबंधित प्रश्न
If A and B are (−2, −2) and (2, −4), respectively, find the coordinates of P such that `"AP" = 3/7 "AB"` and P lies on the line segment AB.
Find the coordinates of the points which divide the line segment joining A (−2, 2) and B (2, 8) into four equal parts.
Calculate the ratio in which the line joining A(6, 5) and B(4, –3) is divided by the line y = 2.
If A = (−4, 3) and B = (8, −6)
- Find the length of AB.
- In what ratio is the line joining A and B, divided by the x-axis?
A (–3, 4), B (3, –1) and C (–2, 4) are the vertices of a triangle ABC. Find the length of line segment AP, where point P lies inside BC, such that BP : PC = 2 : 3.
A (30, 20) and B ( 6, -4) are two fixed points. Find the coordinates of a point Pin AB such that 2PB = AP. Also, find the coordinates of some other point Qin AB such that AB = 6 AQ.
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.
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`
A line intersects y-axis and x-axis at point P and Q, respectively. If R(2, 5) is the mid-point of line segment PQ, them find the coordinates of P and Q.
