You can use the Pythagorean Theorem to prove the Distance Formula. Let points P(x1, y1 ) and Q(x2 , y2) be the endpoints of the hypotenuse of a right triangle. a. Write an algebraic expression to complete each of the following: PR = ? and QR = ? . b. By the Pythagorean Theorem, PQ squared = PR squared + QR squared . Rewrite this statement by substituting the algebraic expressions you found for PR and QR in part (a) c. Complete the proof by taking the square root of each side of the equation that you wrote in part (b).
You can use the Pythagorean Theorem to prove the Distance Formula. Let points P(x1, y1 ) and Q(x2 , y2) be the endpoints of the hypotenuse of a right triangle. a. Write an algebraic expression to complete each of the following: PR = ? and QR = ? . b. By the Pythagorean Theorem, PQ squared = PR squared + QR squared . Rewrite this statement by substituting the algebraic expressions you found for PR and QR in part (a) c. Complete the proof by taking the square root of each side of the equation that you wrote in part (b).
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter9: Real Numbers And Right Triangles
Section9.5: The Distance And Midpoint Formulas
Problem 51E
Related questions
Question
You can use the Pythagorean Theorem to prove the Distance Formula. Let points P(x1, y1 ) and Q(x2 , y2) be the endpoints of the hypotenuse of a right
a. Write an algebraic expression to complete each of the following: PR = ? and QR = ? .
b. By the Pythagorean Theorem, PQ squared = PR squared + QR squared . Rewrite this statement by substituting the algebraic expressions you found for PR and QR in part (a)
c. Complete the proof by taking the square root of each side of the equation that you wrote in part (b).
AI-Generated Solution
Unlock instant AI solutions
Tap the button
to generate a solution
Recommended textbooks for you
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Algebra: Structure And Method, Book 1](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9780998625720/9780998625720_smallCoverImage.gif)
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Algebra: Structure And Method, Book 1](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9780998625720/9780998625720_smallCoverImage.gif)
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill