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What is the distance in the standard (x, y) coordinate plane between the points (2,3) and (5,5)?
- a)3
- b)5
- c)√11
- d)√13
- e)√25
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
What is the distance in the standard (x, y) coordinate plane between t...
The correct answer is D.
To find the distance between 2 points in the standard (x, y) coordinate plane, use the distance formula, which states that
d =
.
Therefore, the distance is
which equals (32 + 22), which equals √13.
Another way to look at this problem would be to draw a picture as shown above. Then you can use the Pythagorean Theorem to find the hypotenuse of the triangle that is formed from the given points.
To find the distance between 2 points in the standard (x, y) coordinate plane, use the distance formula, which states that
d =
.Therefore, the distance is
which equals (32 + 22), which equals √13.Another way to look at this problem would be to draw a picture as shown above. Then you can use the Pythagorean Theorem to find the hypotenuse of the triangle that is formed from the given points.
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What is the distance in the standard (x, y) coordinate plane between t...
Understanding Distance in the Coordinate Plane
To find the distance between two points in the (x, y) coordinate plane, we use the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
Given Points
- Point A (x1, y1) = (2, 3)
- Point B (x2, y2) = (5, 5)
Calculating the Differences
- x2 - x1 = 5 - 2 = 3
- y2 - y1 = 5 - 3 = 2
Applying the Distance Formula
Now, substitute the differences into the distance formula:
1. Square the differences:
- (x2 - x1)² = 3² = 9
- (y2 - y1)² = 2² = 4
2. Add the squared differences:
- 9 + 4 = 13
3. Take the square root:
- Distance = √(13)
Final Result
Thus, the distance between the points (2, 3) and (5, 5) is √13, which corresponds to option 'D'.
This distance represents how far apart the two points are in the coordinate plane, and using the distance formula is a standard method for these calculations.
To find the distance between two points in the (x, y) coordinate plane, we use the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
Given Points
- Point A (x1, y1) = (2, 3)
- Point B (x2, y2) = (5, 5)
Calculating the Differences
- x2 - x1 = 5 - 2 = 3
- y2 - y1 = 5 - 3 = 2
Applying the Distance Formula
Now, substitute the differences into the distance formula:
1. Square the differences:
- (x2 - x1)² = 3² = 9
- (y2 - y1)² = 2² = 4
2. Add the squared differences:
- 9 + 4 = 13
3. Take the square root:
- Distance = √(13)
Final Result
Thus, the distance between the points (2, 3) and (5, 5) is √13, which corresponds to option 'D'.
This distance represents how far apart the two points are in the coordinate plane, and using the distance formula is a standard method for these calculations.
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What is the distance in the standard (x, y) coordinate plane between the points (2,3) and (5,5)?a)3b)5c)√11d)√13e)√25Correct answer is option 'D'. Can you explain this answer?
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