2019 AMC 8 Problems/Problem 21: Difference between revisions
| Line 1: | Line 1: | ||
==Problem 21== | ==Problem 21== | ||
What is the area of the triangle formed by the lines <math>y=5</math>, <math>y=1+x</math>, and <math> | What is the area of the triangle formed by the lines <math>y=5</math>, <math>y=1+x</math>, and <math>y=1-x</math>? | ||
<math>\textbf{(A) }4\qquad\textbf{(B) }8\qquad\textbf{(C) }10\qquad\textbf{(D) }12\qquad\textbf{(E) }16</math> | <math>\textbf{(A) }4\qquad\textbf{(B) }8\qquad\textbf{(C) }10\qquad\textbf{(D) }12\qquad\textbf{(E) }16</math> | ||
Revision as of 17:02, 20 November 2019
Problem 21
What is the area of the triangle formed by the lines 
, 
, and 
?
Solution 1
You need to first find the coordinates where the graphs intersect. y=5, and y=x+1 intersect at (4,5). y=5, and y=1-x intersect at (-4,5). y=1-x and y=1+x intersect at (1,0). Using the Shoelace Theorem you get ![\[\left(\frac{(20-4)-(-20+4)}{2}\right)\]](http://latex.artofproblemsolving.com/8/1/9/81958394559aa60a28897e9a3df25fce2ce74b15.png)
=
\boxed{\textbf{(E)}\ 16}$.
See Also
| 2019 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
