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प्रश्न
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.
पर्याय
AP = \[\frac{1}{3}\text{AB}\]
AP = PB
PB = \[\frac{1}{3}\text{AB}\]
- AP = \[\frac{1}{2}\text{AB}\]
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उत्तर
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then `underlinebb(AP = 1/2 AB)`.
Explanation:
Given that, the point P(2, 1) lies on the line segment joining the points A(4, 2) and B(8, 4), which shows in the figure below:
Now, distance between A(4, 2) and P(2, 1),
AP = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AP = `sqrt((2 - 4)^2 + (1 -2)^2`
= `sqrt((-2)^2 + (-1)^2`
= `sqrt(4 + 1)`
= `sqrt(5)`
Distance between A(4, 2) and B(8, 4),
AB = `sqrt((8 - 4)^2 + (4 - 2)^2`
= `sqrt((4)^2 + (2)^2`
= `sqrt(16 + 4)`
= `sqrt(20)`
= `2sqrt(5)`
Distance between B(8, 4) and P(2, 1),
BP = `sqrt((8 - 2)^2 + (4 - 1)^2`
= `sqrt(6^2 + 3^2`
= `sqrt(36 + 9)`
= `sqrt(45)`
= `3sqrt(5)`
∴ AB = `2sqrt(5)`
= 2AP
⇒ AP = `"AB"/2`
Hence, required condition is AP = `"AB"/2`
संबंधित प्रश्न
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Find the value of a when the distance between the points (3, a) and (4, 1) is `sqrt10`
Find the distance of the following points from the origin:
(iii) C (-4,-6)
Find all possible values of x for which the distance between the points
A(x,-1) and B(5,3) is 5 units.
Find the value of m if the distance between the points (m , -4) and (3 , 2) is 3`sqrt 5` units.
Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.
Prove that the points (5 , 3) , (1 , 2), (2 , -2) and (6 ,-1) are the vertices of a square.
In what ratio does the point P(−4, y) divides the line segment joining the points A(−6, 10) and B(3, −8)? Hence find the value of y.
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By using the distance formula prove that each of the following sets of points are the vertices of a right angled triangle.
(i) (6, 2), (3, -1) and (- 2, 4)
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Using distance formula,
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|
Alia and Shagun are friends living on the same street in Patel Nagar. Shagun's house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C. |
Based on the above information, answer the following questions.
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- Show that for Shagun, school is farther compared to Alia's house and library.
OR
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