The soccer field question confuses me - I don't understand how =√52 becomes 2√13! Any help?

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.

Dont understand the graph

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.

what is the Pythagorean therom

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

how do you use the Pythagorean Theorem

The Pythagorean Theorem is used to find the side length of RIGHT triangles. THIS CAN NOT BE USED FOR ANY OTHER TYPE OF TRIANGLE! You take the length of side a(the side that creates a right angle) and square it. Then add it to side b squared(the other side creating a right angle) and this will give you the value of c sqaured. Now square root this value to get the length of side c, or the hypotenuse, which is perpendicular to the right angle. Hope this helps!

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?

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

Am I allowed to use trigonometry to solve these?

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.

Main content

High school geometry

Course: High school geometry > Unit 6

Lesson 1: Distance and midpoints

Distance formula review

Google Classroom

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

What is the distance formula?

The formula gives the distance between two points left parenthesis, start color #1fab54, x, start subscript, 1, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 1, end subscript, end color #e07d10, right parenthesis and left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis on the coordinate plane:

square root of, left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, minus, x, start subscript, 1, end subscript, end color #1fab54, right parenthesis, squared, plus, left parenthesis, start color #e07d10, y, start subscript, 2, end subscript, minus, y, start subscript, 1, end subscript, end color #e07d10, right parenthesis, squared, end square root

It is derived from the Pythagorean theorem.

Want to learn more about the distance formula? Check out this video.

What problems can I solve with the distance formula?

Given two points on the plane, you can find their distance. For example, let's find the distance between left parenthesis, start color #1fab54, 1, end color #1fab54, comma, start color #e07d10, 2, end color #e07d10, right parenthesis and left parenthesis, start color #1fab54, 9, end color #1fab54, comma, start color #e07d10, 8, end color #e07d10, right parenthesis:

\begin{aligned} &\phantom{=}\sqrt{(\greenD{x_2 - x_1})^2 + (\goldD{y_2 - y_1})^2} \\\\ &=\sqrt{(\greenD{9 -1})^2 + (\goldD{8 - 2})^2}\quad\small\gray{\text{Plug in coordinates}} \\\\ &=\sqrt{8^2+6^2} \\\\ &=\sqrt{100} \\\\ &=10 \end{aligned}

Notice: we were careful to put the x-coordinates together and the y-coordinates together and not mix them up.

Check your understanding

Problem 1

Current

What is the distance between left parenthesis, 4, comma, 2, right parenthesis and left parenthesis, 8, comma, 5, right parenthesis?

Want to try more problems like this? Check out this exercise.

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17017
Posted 5 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?
Button navigates to signup pageComment on 17017's post “The soccer field question...”
(33 votes)
Answer
- Ian Pulizzotto
  Posted 5 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 ...”
  (91 votes)
kristofer
Posted 5 years ago. Direct link to kristofer's post “what is the Pythagorean t...”
what is the Pythagorean therom
Button navigates to signup pageComment on kristofer's post “what is the Pythagorean t...”
(3 votes)
Answer
- Daniel Ye
  Posted 5 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
  Comment on Daniel Ye's post “The pythagorean therom st...”
  (15 votes)
792569
Posted 3 years ago. Direct link to 792569's post “how do u solve it if the ...”
how do u solve it if the 2 x's are negetavie
Button navigates to signup pageComment on 792569's post “how do u solve it if the ...”
(5 votes)
Answer
- Monil Mehta
  Posted 6 months ago. Direct link to Monil Mehta's post “You can still subtract a ...”
  You can still subtract a negative from a negative. -3-(-6) is the same as -3+6, which is three. If you instead do -6-(-3), it's the same as -6+3, which is -3. Either works as you will be squaring it, which is a positive number anyways. Hope this helps!
  Comment on Monil Mehta's post “You can still subtract a ...”
  (1 vote)
Mateo Bump
Posted a year 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?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Jerry Nilsson
  Posted a year 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, ...”
  (9 votes)
349933
Posted 3 years ago. Direct link to 349933's post “Dont understand the graph”
Dont understand the graph
Button navigates to signup pageComment on 349933's post “Dont understand the graph”
(4 votes)
Answer
- BraedenHill001
  Posted 2 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.
  Button navigates to signup page
  (2 votes)
Riley Woodall-gunderman
Posted 5 years ago. Direct link to Riley Woodall-gunderman's post “how do you use the Pythag...”
how do you use the Pythagorean Theorem
Button navigates to signup pageComment on Riley Woodall-gunderman's post “how do you use the Pythag...”
(2 votes)
Answer
- Paree Nagda
  Posted 5 years ago. Direct link to Paree Nagda's post “The Pythagorean Theorem i...”
  The Pythagorean Theorem is used to find the side length of RIGHT triangles. THIS CAN NOT BE USED FOR ANY OTHER TYPE OF TRIANGLE! You take the length of side a(the side that creates a right angle) and square it. Then add it to side b squared(the other side creating a right angle) and this will give you the value of c sqaured. Now square root this value to get the length of side c, or the hypotenuse, which is perpendicular to the right angle. Hope this helps!
  Button navigates to signup page
  (4 votes)
eva stepherson
Posted 3 years ago. Direct link to eva stepherson's post “It all confuses me. But m...”
It all confuses me. But mostly the soccer feild.
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(3 votes)
Answer
victoramalraj1966
Posted 6 years ago. Direct link to victoramalraj1966's post “find a point on the y axi...”
find a point on the y axis which is equidistant from the points [5,2] and [-4,3]
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(4 votes)
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- saipra003
  Posted 6 years ago. Direct link to saipra003's post “After finding the prime f...”
  After finding the prime factorization you have to eliminate the 2's since there are 2 of them and put them outside the radical.
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  (0 votes)
Quinn Hays
Posted 10 months 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)
Answer
- David Severin
  Posted 10 months 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.
  Button navigates to signup page
  (4 votes)
Faith Metaxotos
Posted 3 years ago. Direct link to Faith Metaxotos's post “im just confused how 52 t...”
im just confused how 52 turned into 2times the square route of 13. it doesnt explain why, it just expects you to understand it.
Button navigates to signup pageComment on Faith Metaxotos's post “im just confused how 52 t...”
(2 votes)
Answer
- Ian Pulizzotto
  Posted 3 years ago. Direct link to Ian Pulizzotto's post “I believe you meant the s...”
  I believe you meant the square root of 52, not 52 itself.
  
  Because 52=4*13 and the square root of a product of non-negative numbers is always the product of the square roots, we have
  
  sqrt(52) = sqrt(4*13) = sqrt(4)*sqrt(13) = 2sqrt(13).
  Button navigates to signup page
  (1 vote)