What is the distance formula in geometry?

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x 2 – x 1 )² + (y 2 – y 1 )²) . This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

What is the application of distance formula?

The distance formula is derived using mathematician Pythagoras's theorem, Pythagoras Theorem. It has various applications in daily life. It is used in navigation . The pilot of a plane calculates the distance between their plane and the other plane using the distance formula.

What is the distance formula for analytic geometry Khan Academy?

Learn how to find the distance between two points by using the distance formula, which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points.

What is the formula for the longest distance between two points?

The distance between two points can be calculated using the following steps, Denote the given points as (x 1 , y 1 ) and (x 2 , y 2 ). Apply the Euclidean distance formula, distance, d = √[(x 2 − x 1 ) 2 + (y 2 − y 1 ) 2 ]

Distance formula review | Analytic geometry (article)

Review the distance formula and how to apply it to solve problems.

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17017
6 years agoPosted 6 years ago. Direct link to 17017's post “The soccer field question...”
The soccer field question confuses me - I don't understand how =√52 becomes 2√13!
Any help?
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(41 votes)
- Ian Pulizzotto
  6 years agoPosted 6 years ago. Direct link to Ian Pulizzotto's post “To simplify √52, we look ...”
  To simplify √52, we look for the largest perfect square factor of 52. This factor is 4.
  Since the square root of a product of positive numbers is the product of their square roots,
  √52 = √(4*13) =√4 * √13 = 2√13.
  Comment on Ian Pulizzotto's post “To simplify √52, we look ...”
  (119 votes)
kristofer
7 years agoPosted 7 years ago. Direct link to kristofer's post “what is the Pythagorean t...”
what is the Pythagorean therom
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(5 votes)
- Daniel Ye
  6 years agoPosted 6 years ago. Direct link to Daniel Ye's post “The pythagorean therom st...”
  The pythagorean therom states that a^2 + b^2 = c^2. Or, the sum of the two short sides of the right triangle squared = the hypotunuse (the long side of the right triangle) squared
  NOTE: this works and ONLY WORKS FOR A RIGHT TRIANGLE. It does NOT and CAN'T apply to any other type of triangle
  See Also
  8.2: Distance and Midpoint Formulas and Circles Section 1.1 The Distance and Midpoint Formulas
  Comment on Daniel Ye's post “The pythagorean therom st...”
  (22 votes)
Remedy
a year agoPosted a year ago. Direct link to Remedy's post “I have a question about t...”
I have a question about the last problem. Simplify one of the distances and the final formula is 2√13 + √13, but I didn't know the same number of square roots can be combined. Does anyone know where I can learn about it?
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(4 votes)
- David Severin
  a year agoPosted a year ago. Direct link to David Severin's post “anytime you can substitut...”
  anytime you can substitute an x, you may be able to simplify. Let x=√13, this gives 2x + x, and hopefully you understand by now that you can combine like terns to get 3x. Substitutin back in, you get 3√13.
  Comment on David Severin's post “anytime you can substitut...”
  (10 votes)
Quinn Hays
2 years agoPosted 2 years ago. Direct link to Quinn Hays's post “Am I allowed to use trigo...”
Am I allowed to use trigonometry to solve these?
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(1 vote)
- David Severin
  2 years agoPosted 2 years ago. Direct link to David Severin's post “If you use trig, it will ...”
  If you use trig, it will be a more indirect way to get the answer, but you can if you want. You would have to find the inverse tan to find the angle, then apply either sin or cos to find the third side.
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  (12 votes)
349933
4 years agoPosted 4 years ago. Direct link to 349933's post “Dont understand the graph”
Dont understand the graph
Button navigates to signup page•Comment on 349933's post “Dont understand the graph”
(5 votes)
- BraedenHill001
  4 years agoPosted 4 years ago. Direct link to BraedenHill001's post “The graph is showing the ...”
  The graph is showing the x and y coordinates of the three points so that you can find the differences in x and y. Once you have found the difference in x and y, you can then solve using the Pythagorean Theorem.
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  (3 votes)
kpop0215
10 months agoPosted 10 months ago. Direct link to kpop0215's post “Why is the exponent at th...”
Why is the exponent at the bottom?
Button navigates to signup page•Comment on kpop0215's post “Why is the exponent at th...”
(3 votes)
- Bani Hundal
  10 months agoPosted 10 months ago. Direct link to Bani Hundal's post “This is not an exponent, ...”
  This is not an exponent, it just shows the order.
  Button navigates to signup page
  (6 votes)
Dayton
8 months agoPosted 8 months ago. Direct link to Dayton's post “I find it so funny that t...”
I find it so funny that the khan comments are so harmonic.
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(5 votes)
Mateo Bump
2 years agoPosted 2 years ago. Direct link to Mateo Bump's post “Hello, I Don't understand...”
Hello, I Don't understand the distance between(2,2) and (4,7) I'm very confused and i'm good at math but wow.
Any help?
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(0 votes)
- Jerry Nilsson
  2 years agoPosted 2 years ago. Direct link to Jerry Nilsson's post “The two points are (𝑥₁, ...”
  The two points are (𝑥₁, 𝑦₁) = (2, 2) and (𝑥₂, 𝑦₂) = (4, 7)
  The distance formula tells us
  𝑑 = √((𝑥₁ − 𝑥₂)² + (𝑦₁ − 𝑦₂)²)
  = √((2 − 4)² + (2 − 7)²)
  = √((−2)² + (−5)²)
  = √(4 + 25)
  = √29
  Comment on Jerry Nilsson's post “The two points are (𝑥₁, ...”
  (13 votes)
eva stepherson
4 years agoPosted 4 years ago. Direct link to eva stepherson's post “It all confuses me. But m...”
It all confuses me. But mostly the soccer feild.
Button navigates to signup page•Comment on eva stepherson's post “It all confuses me. But m...”
(5 votes)
XxGl1tchxX
10 months agoPosted 10 months ago. Direct link to XxGl1tchxX's post “Are there any quick and e...”
Are there any quick and easy ways to remember the Distance Formula? It's so long! I find it very hard to remember!!
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(2 votes)
- Ian Pulizzotto
  10 months agoPosted 10 months ago. Direct link to Ian Pulizzotto's post “The distance formula is e...”
  The distance formula is easier to remember if you observe that it comes from the Pythagorean theorem.
  Imagine a right triangle with vertices at (x_1, y_1), (x_2, y_1), and (x_2, y_2). The legs have lengths |x_2 - x_1| and |y_2 - y_1|, and the hypotenuse is the distance between (x_1, y_1) and (x_2, y_2). The distance formula then follows from using the Pythagorean theorem on this right triangle.
  Have a blessed, wonderful day!
  Comment on Ian Pulizzotto's post “The distance formula is e...”
  (5 votes)

Distance formula review | Analytic geometry (article) | Khan Academy (2024)

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