Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

The length of a line segment is 7. Its end points are (1, 3) and (k, 3). Solve for k. Is there more than one solution? Explain.

Sagot :

luana
[tex]Endpoints:\\\\A(1,3)\ and\ B(k,3)\\\\Formula\ for\ length\ of\ line:\\\\ |AB|=\sqrt{(x_b-x_a)^2+(y_b-y_a)^2}\\\\ |AB|=7\\\\7=\sqrt{(k-1)^2+(3-3)^2}\\\\ 7=\sqrt{k^2-2k-1}\ \ |^2\\\\ 49=k^2-2k-1 [/tex][tex]49=k^2-2k-1\\\\ -k^2+2k+1+49=0\\\\ -k^2+2k+50=0\\\\ \Delta=b^2-4ac\\\\a=-1,\ b=2,\ c=50 \\\\\Delta=(2)^2-4*(-1)*50=4-=4+200=204\\\\ \sqrt{\Delta}=2\sqrt{51}[/tex][tex]\\\\k_1=\frac{-b-\sqrt{\Delta}}{2a}\ \ k_1=\frac{-2-2\sqrt{51}}{2*(-1)}=1+\sqrt{51} \\\\\ or\ k_2=\frac{-b+\sqrt{\Delta}}{2a}\ \ k_1=\frac{-2+2\sqrt{51}}{2*(-1)}=1-\sqrt{51}[/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.