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प्रश्न
In what ratio is the line joining (2, –4) and (–3, 6) divided by the y-axis?
उत्तर
Let the line joining points A (2, –4) and B (–3, 6) be divided by point P (0, y) in the ratio k : 1.
`x = (kx_2 + x_1)/(k + 1)`
`0 = (k xx (-3) + 1 xx 2)/(k + 1)`
`0 = -3k + 2`
`k = 2/3`
Thus, the required ratio is 2 : 3.
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संबंधित प्रश्न
In what ratio is the line joining (2, –3) and (5, 6) divided by the x-axis?
Find the ratio in which the line 2x + y = 4 divides the line segment joining the point P(2, –2) and Q(3, 7).
Find the image of the point A(5, –3) under reflection in the point P(–1, 3).
Find the image of the point A(5,3) under reflection in the point P(-1,3).
Find the image of the point A(5,3) under reflection in the point P(-1,3).
Prove that the points A(-5, 4), B(-1, -2) and C(S, 2) are the vertices of an isosceles right-angled triangle. Find the coordinates of D so that ABCD is a square.
The line segment joining A (2, 3) and B (6, – 5) is intersected by the X axis at the point K. Write the ordinate of the point K. Hence find the ratio in which K divides AB.
Show that the points A(1, 3), B(2, 6), C(5, 7) and D(4, 4) are the vertices of a rhombus.
= `a(1/t^2 + 1) = (a(t^2 + 1))/t^2`
Now `(1)/"SP" + (1)/"SQ" = (1)/(a(t^2 + 1)) + (1 xx t^2)/(a(t^2 + 1)`
= `((1 + t^2))/(a(t^2 + 1)`
`(1)/"SP" + (1)/"SQ" = (1)/a`.
If the line joining the points A(4, - 5) and B(4, 5) is divided by the point P such that `"AP"/"AB" = (2)/(5)`, find the coordinates of P.
In the following figure line APB meets the X-axis at A, Y-axis at B. P is the point (4, -2) and AP: PB = 1: 2. Write down the coordinates of A and B.
