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प्रश्न
The ratio in which the x-axis divides the line segment joining the points A (a1, b1) and B (a2, b2) is
विकल्प
b1 : b2
−b1 : b2
a1 : a2
−a1 : a2
उत्तर
−b1 : b2
Explanation;
Hint:
A line divides internally in the ratio m : n the point P is, `(("m"x_2 + "n"x_1)/("m" + "n"), ("m"_2 +"n"y_1)/("m" + "n"))`
The point P is (a, 0) = `(("ma"_2 + "na"_1)/("m" + "n"), ("mb"_2 + "nb"_1)/("m" "n"))`
∴ `("mb"_2 + "nb"_1)/("m" + "n")` = 0
mb2 + nb1 = 0
⇒ mb2 = −nb1
`"m"/"n" = "b"_1/"b"_2`
∴ m : n = −b1 : b2
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संबंधित प्रश्न
Find the mid-point of the line segment joining the points:
(5, –3) and (–1, 7)
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Prove that the points A(–5, 4); B(–1, –2) and C(5, 2) are the vertices of an isosceles right-angled triangle. Find the co-ordinates of D so that ABCD is a square.
Find the coordinates of point P if P divides the line segment joining the points A(–1, 7) and B(4, –3) in the ratio 2 : 3.
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From the figure given alongside, find the length of the median AD of triangle ABC. Complete the activity.
Solution:
Here A(–1, 1), B(5, – 3), C(3, 5) and suppose D(x, y) are coordinates of point D.
Using midpoint formula,
x = `(5 + 3)/2`
∴ x = `square`
y = `(-3 + 5)/2`
∴ y = `square`
Using distance formula,
∴ AD = `sqrt((4 - square)^2 + (1 - 1)^2`
∴ AD = `sqrt((square)^2 + (0)^2`
∴ AD = `sqrt(square)`
∴ The length of median AD = `square`
