Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Find the distance between the pair of parallel lines, y = x-11 & y = x-7

Sagot :

kate200468
[tex]k:\ y = x-11\ \ \ \Leftrightarrow\ \ \ x-y-11=0\\ and\\ l:\ y = x-7\ \ \ \Leftrightarrow\ \ \ x-y-7=0\\\\the\ distance:\\\\ d(k;l)= \frac{\big{|-11-(-7)|}}{\big{ \sqrt{1^2+1^2} }} =\frac{\big{|-11+7|}}{\big{ \sqrt{2} }} =\frac{\big{|-4|}}{\big{ \sqrt{2} }} =\frac{\big{4\cdot \sqrt{2} }}{\big{ \sqrt{2}\cdot \sqrt{2} }} =\frac{\big{4 \sqrt{2} }}{\big{2 }} =2 \sqrt{2} [/tex]
Lilith
[tex]Given \ the \ equations \ of \ two \ non-vertical \ parallel \ lines:\\\\y = mx+b_1\\y = mx+b_2\\\\the \ distance \ between \ them \ can \ be \ expressed \ as : \\\\d= \frac{|b_{1}-b_{2}|}{ \sqrt{ m^2+1} }[/tex]

[tex]y = x-11 \\ y = x-7 \\\\\\d= \frac{| -11- (-7)|}{ \sqrt{ 1^2+1} } =\frac{| -11+7|}{ \sqrt{ 1+1} } = \frac{|-4|}{ \sqrt{2} } = \frac{4}{ \sqrt{2} }\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}[/tex]
 

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.