<p>The graphs of <img alt="$y = -|x-a| + b$" height="18" src="https://latex.artofproblemsolving.com/9/8/c/98c7b0888bd4f62553212887fee4136bbdfa470b.png" width="130" /> and <img alt="$y = |x-c| + d$" height="18" src="https://latex.artofproblemsolving.com/3/9/1/3919aa9305e70a777b00ba4d5067bd85a278509e.png" width="116" /> intersect at points <img alt="$(2,5)$" height="18" src="https://latex.artofproblemsolving.com/e/a/9/ea9d3308a17610dcb38bfd84b443bdd0ea403605.png" width="38" /> and <img alt="$(8,3)$" height="18" src="https://latex.artofproblemsolving.com/9/1/f/91f8c8232fd46a61eca8423bbd3cec33adb70e74.png" width="38" />. Find <img alt="$a+c$" height="12" src="https://latex.artofproblemsolving.com/f/b/8/fb837dc059a93f257aed66ef84d279c516fca180.png" width="40" />.</p>

Question No: 233

The graphs of $y = -|x-a| + b$ and $y = |x-c| + d$ intersect at points $(2,5)$ and $(8,3)$ . Find $a+c$ .

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Tags: Algebra Geometry

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