Difference between revisions of "2005 iTest Problems/Problem 9"
(Created page with "==Problem== Find the area of the triangle with vertices of <math>(1,2)</math>, <math>(1,10)</math>, and <math>(5, 5)</math>. ==Solution 1== Since <math>(1,2)</math> and <math...") |
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==Solution 1== | ==Solution 1== | ||
Since <math>(1,2)</math> and <math>(1,10)</math> are collinear, let that be the base. It therefore has length 8. The distance from <math>(5, 5)</math> to this line is the same as the distance from <math>(5,5)</math> to <math>(1,5)</math>, which is equal to 4. The area of this triangle is <math>\frac{8\cdot4}{2}=\boxed{16}</math>. | Since <math>(1,2)</math> and <math>(1,10)</math> are collinear, let that be the base. It therefore has length 8. The distance from <math>(5, 5)</math> to this line is the same as the distance from <math>(5,5)</math> to <math>(1,5)</math>, which is equal to 4. The area of this triangle is <math>\frac{8\cdot4}{2}=\boxed{16}</math>. | ||
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| + | ==See Also== | ||
| + | {{iTest box|year=2005|num-b=8|num-a=10}} | ||
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| + | [[Category: Introductory Geometry Problems]] | ||
Latest revision as of 18:01, 13 October 2025
Problem
Find the area of the triangle with vertices of 
, 
, and 
.
Solution 1
Since and are collinear, let that be the base. It therefore has length 8. The distance from to this line is the same as the distance from 
to 
, which is equal to 4. The area of this triangle is 
.
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 8 |
Followed by: Problem 10 | |
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