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प्रश्न
The distance between the points (0, 5) and (–5, 0) is ______.
पर्याय
5
`5sqrt2`
`2sqrt(5)`
10
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उत्तर
The distance between the points (0, 5) and (–5, 0) is `underlinebb(5sqrt2)`.
Explanation:
Distance formula: d2 = (x2 – x1)2 + (y2 – y1)2
According to the question,
We have,
x1 = 0, x2 = – 5
y1 = 5, y2 = 0
d2 = ((– 5) – 0)2 + (0 – 5)2
d = `sqrt((-5 - 0)^2 + (0 - 5)^2`
d = `sqrt((-5)^2 + (-5)^2`
d = `sqrt(25 + 25)`
d = `sqrt(50) = 5sqrt(2)`
So the distance between (0, 5) and (–5, 0) = `5sqrt(2)`
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Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
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- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
The coordinates of the centroid of ΔEHJ are ______.
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