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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 does the point (1, a) divide the join of (–1, 4) and (4, –1)? Also, find the value of a.
Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x
If the abscissa of a point P is 2, find the ratio in which this point divides the line segment joining the point (−4, 3) and (6, 3). Also, find the co-ordinates of point P.
The line joining the points (2, 1) and (5, –8) is trisected at the point P and Q. If point P lies on the line 2x – y + k = 0, find the value of k. Also, find the co-ordinates of point Q.
M is the mid-point of the line segment joining the points A(0, 4) and B(6, 0). M also divides the line segment OP in the ratio 1 : 3. Find :
- co-ordinates of M
- co-ordinates of P
- length of BP
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`.
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.
