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2005 iTest Problems/Problem 9

Revision as of 16:34, 13 October 2025 by Mathloveryeah (talk | contribs) (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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Problem

Find the area of the triangle with vertices of $(1,2)$, $(1,10)$, and $(5, 5)$.

Solution 1

Since $(1,2)$ and $(1,10)$ are collinear, let that be the base. It therefore has length 8. The distance from $(5, 5)$ to this line is the same as the distance from $(5,5)$ to $(1,5)$, which is equal to 4. The area of this triangle is $\frac{8\cdot4}{2}=\boxed{16}$.