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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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Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane. |
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[or]
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