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प्रश्न
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.
उत्तर
A (2, 3) and B (6,- 5)
Intersected at X axis at K.
∴ y = 0 or ordinate = 0
K (x, 0)
Let required ratio be a: 1
∴ Ordinate of K = 0
0 = `(a xx -5 + 1 xx 3)/(a + 1)`
0 = -5a + 3
5a = 3, a = `(3)/(5)`
∴ K divides AB in ratio of 3 : 5.
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संबंधित प्रश्न
Calculate the co-ordinates of the point P which divides the line segment joining: A (–4, 6) and B (3, –5) in the ratio 3 : 2
In what ratio is the line joining (2, –3) and (5, 6) divided by the x-axis?
In what ratio is the line joining (2, –4) and (–3, 6) divided by the y-axis?
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
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).
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`.
The midpoint of the line segment AB shown in the diagram is (4, – 3). Write down the coordinates of A and B.
From the adjacent figure:
(i) Write the coordinates of the points A, B, and
(ii) Write the slope of the line AB.
(iii) Line through C, drawn parallel to AB, intersects Y-axis at D. Calculate the co-ordinates of D.
