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प्रश्न
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.
उत्तर
Let R (x, -1) be the point on the line y = - 1 which divides the line segment PQ in the ratio k: 1.
Coordinates of R are,
x = `(2"k" + 6)/("k" + 1) ,` -1 = `(-11 "k" + 5)/("k" + 1)`
x = `(-2 (3/5) + 6)/(3/5 + 1), => - "k" - 1 = - 11 "k" + 5`
`=> "x" = (-6 + 30)/8 => 10 "k" = 6`
x = 3 ⇒ k = 3/5 .....(1)
Hence, the required ratio is 3: 5 and the point of inter sec tion is (3, - 1).
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संबंधित प्रश्न
Find the ratio in which y-axis divides the line segment joining the points A(5, –6) and B(–1, –4). Also find the coordinates of the point of division.
Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7)
If two vertices of a parallelogram are (3, 2) (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.
A (2, 5), B (–1, 2) and C (5, 8) are the co-ordinates of the vertices of the triangle ABC. Points P and Q lie on AB and AC respectively, such that : AP : PB = AQ : QC = 1 : 2.
- Calculate the co-ordinates of P and Q.
- Show that : `PQ = 1/3 BC`.
The line segment joining A(4, 7) and B(−6, −2) is intercepted by the y – axis at the point K. write down the abscissa of the point K. hence, find the ratio in which K divides AB. Also, find the co-ordinates of the point K.
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 coordinate of a point P which divides the line segment joining :
5(2, 6) and R(9, -8) in the ratio 3: 4.
The points A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC. The median from A meets BC at D. Find the coordinates of the point D.
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.
