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Question
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.
Options
AP = \[\frac{1}{3}\text{AB}\]
AP = PB
PB = \[\frac{1}{3}\text{AB}\]
- AP = \[\frac{1}{2}\text{AB}\]
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Solution
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`
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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. |
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OR
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