\documentclass[10pt,a4paper]{article} % Packages \usepackage{fancyhdr} % For header and footer \usepackage{multicol} % Allows multicols in tables \usepackage{tabularx} % Intelligent column widths \usepackage{tabulary} % Used in header and footer \usepackage{hhline} % Border under tables \usepackage{graphicx} % For images \usepackage{xcolor} % For hex colours %\usepackage[utf8x]{inputenc} % For unicode character support \usepackage[T1]{fontenc} % Without this we get weird character replacements \usepackage{colortbl} % For coloured tables \usepackage{setspace} % For line height \usepackage{lastpage} % Needed for total page number \usepackage{seqsplit} % Splits long words. %\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely. \usepackage[normalem]{ulem} % For underlining links % Most of the following are not required for the majority % of cheat sheets but are needed for some symbol support. \usepackage{amsmath} % Symbols \usepackage{MnSymbol} % Symbols \usepackage{wasysym} % Symbols %\usepackage[english,german,french,spanish,italian]{babel} % Languages % Document Info \author{Ebrahim.O} \pdfinfo{ /Title (co-ordinate-geometry-and-simultaneous-equations.pdf) /Creator (Cheatography) /Author (Ebrahim.O) /Subject (Co-Ordinate Geometry \& Simultaneous Equations Cheat Sheet) } % Lengths and widths \addtolength{\textwidth}{6cm} \addtolength{\textheight}{-1cm} \addtolength{\hoffset}{-3cm} \addtolength{\voffset}{-2cm} \setlength{\tabcolsep}{0.2cm} % Space between columns \setlength{\headsep}{-12pt} % Reduce space between header and content \setlength{\headheight}{85pt} % If less, LaTeX automatically increases it \renewcommand{\footrulewidth}{0pt} % Remove footer line \renewcommand{\headrulewidth}{0pt} % Remove header line \renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit % This two commands together give roughly % the right line height in the tables \renewcommand{\arraystretch}{1.3} \onehalfspacing % Commands \newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour \newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols \newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns \newcommand{\tn}{\tabularnewline} % Required as custom column type in use % Font and Colours \definecolor{HeadBackground}{HTML}{333333} \definecolor{FootBackground}{HTML}{666666} \definecolor{TextColor}{HTML}{333333} \definecolor{DarkBackground}{HTML}{1F3AC2} \definecolor{LightBackground}{HTML}{F1F2FB} \renewcommand{\familydefault}{\sfdefault} \color{TextColor} % Header and Footer \pagestyle{fancy} \fancyhead{} % Set header to blank \fancyfoot{} % Set footer to blank \fancyhead[L]{ \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{C} \SetRowColor{DarkBackground} \vspace{-7pt} {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}} } \end{tabulary} \columnbreak \begin{tabulary}{11cm}{L} \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Co-Ordinate Geometry \& Simultaneous Equations Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Ebrahim.O} via \textcolor{DarkBackground}{\uline{cheatography.com/133545/cs/27308/}}} \end{tabulary} \end{multicols}} \fancyfoot[L]{ \footnotesize \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{LL} \SetRowColor{FootBackground} \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\ \vspace{-2pt}Ebrahim.O \\ \uline{cheatography.com/ebrahim-o} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 29th March, 2021.\\ Updated 29th March, 2021.\\ Page {\thepage} of \pageref{LastPage}. \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\ \SetRowColor{white} \vspace{-5pt} %\includegraphics[width=48px,height=48px]{dave.jpeg} Measure your website readability!\\ www.readability-score.com \end{tabulary} \end{multicols}} \begin{document} \raggedright \raggedcolumns % Set font size to small. Switch to any value % from this page to resize cheat sheet text: % www.emerson.emory.edu/services/latex/latex_169.html \footnotesize % Small font. \begin{multicols*}{3} \begin{tabularx}{5.377cm}{x{2.9862 cm} x{1.9908 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{{\bf{Sketching Straight Lines}}}} \tn % Row 0 \SetRowColor{LightBackground} Using x \& y intercepts | C cannot be equal to 0 & Gradient - intercept method \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} ax + by = c -{}-\textgreater{} e.g 2x - 5y = 10 & y = mx + c \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} y = 0 when solving x & Horizontal Line \tn % Row Count 5 (+ 1) % Row 3 \SetRowColor{white} 2x - 0 = 10 & gradient = 0 \tn % Row Count 6 (+ 1) % Row 4 \SetRowColor{LightBackground} x = 5 & y = c \tn % Row Count 7 (+ 1) % Row 5 \SetRowColor{white} x = 0 when solving y & Vertical Line \tn % Row Count 8 (+ 1) % Row 6 \SetRowColor{LightBackground} 2(0) - 5y = 10 & gradient = undefined \tn % Row Count 10 (+ 2) % Row 7 \SetRowColor{white} -5y = 10 & x = a \tn % Row Count 11 (+ 1) % Row 8 \SetRowColor{LightBackground} y = 10/-5 & a -{}-\textgreater{} x-intercept \tn % Row Count 13 (+ 2) % Row 9 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{y = -2} \tn % Row Count 14 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{0.8354 cm} x{1.04425 cm} x{1.00248 cm} x{1.29487 cm} } \SetRowColor{DarkBackground} \mymulticolumn{4}{x{5.377cm}}{\bf\textcolor{white}{Finding the equation of a straight line}} \tn % Row 0 \SetRowColor{LightBackground} \seqsplit{Gradient} + \seqsplit{y-intercept} & Gradient + a point (x1, y1) & 2 points (x1, y1) (x2, y2) & Distance between 2 points \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} Sub into \seqsplit{equation} & Sub into equation & 1st find m & Sub into equation \tn % Row Count 6 (+ 3) % Row 2 \SetRowColor{LightBackground} y = mx + c & y - y1 = m(x - x1) & m = y2 - y1/x2 - x1 & AB = √(x2 - x1)$^{\textrm{2}}$ + (y2 - y1)$^{\textrm{2}}$ \tn % Row Count 9 (+ 3) % Row 3 \SetRowColor{white} Example & Example & 2nd sub into equation & Example \tn % Row Count 12 (+ 3) % Row 4 \SetRowColor{LightBackground} c = 5 | m = -1 & m = 2 | (2, -0.5) & y - y1 = m(x - x1) & A = (3, -5) | B = (-2, 1) \tn % Row Count 15 (+ 3) % Row 5 \SetRowColor{white} y = -1x + 5 & y + 0.5 = 2(x - 2) & Example & AB = √(-2 - 3)$^{\textrm{2}}$ + (1 - -5)$^{\textrm{2}}$ \tn % Row Count 18 (+ 3) % Row 6 \SetRowColor{LightBackground} & y + 0.5 = 2x - 4 & (-1, 4) , (5, 2) & AB = √(-5)$^{\textrm{2}}$ + 6$^{\textrm{2}}$ \tn % Row Count 20 (+ 2) % Row 7 \SetRowColor{white} & y = 2x - 4.5 & m = 2 - 4/3 - (-1) & AB = √25 + 36 \tn % Row Count 22 (+ 2) % Row 8 \SetRowColor{LightBackground} & & m = -2/4 -{}-\textgreater{} -1/2 & AB = √61 \tn % Row Count 24 (+ 2) % Row 9 \SetRowColor{white} & & y - 4 = -1/2(x - - 1) & \tn % Row Count 27 (+ 3) % Row 10 \SetRowColor{LightBackground} & & y - 4 = - 1/2x - 1/2 & \tn % Row Count 30 (+ 3) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{5.377cm}{x{0.8354 cm} x{1.04425 cm} x{1.00248 cm} x{1.29487 cm} } \SetRowColor{DarkBackground} \mymulticolumn{4}{x{5.377cm}}{\bf\textcolor{white}{Finding the equation of a straight line (cont)}} \tn % Row 11 \SetRowColor{LightBackground} & & y = - 1/2x + 7/2 & \tn % Row Count 2 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}----} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.73926 cm} x{1.41887 cm} x{1.41887 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Middle point of a line}} \tn % Row 0 \SetRowColor{LightBackground} Middle point of a line & Paralell Lines & \seqsplit{Perpendicular} Lines \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Sub into equation - i.e / means divide & Sub into equation & Sub into equation \tn % Row Count 5 (+ 3) % Row 2 \SetRowColor{LightBackground} M = (x1 + x2/2, y1 + y2/2) & m1 = m2 & m1 x m2 = -1 or m2 = 1/m1 \tn % Row Count 8 (+ 3) % Row 3 \SetRowColor{white} Example & Example - 1st find m (gradient) & Example - 1st find m (gradient) \tn % Row Count 11 (+ 3) % Row 4 \SetRowColor{LightBackground} (3, 5) | (2, 7) & A (4, 13) | B (2, 9) & A (-4, 9) | B (2, -6) \tn % Row Count 13 (+ 2) % Row 5 \SetRowColor{white} M = 3 + 2/2, 5 + 7/2 & mAB = 9 - 13/2 - 4 & mAB = -6 - 9/2 - (-4) \tn % Row Count 15 (+ 2) % Row 6 \SetRowColor{LightBackground} M = (5/2, 12/2) & mAB = -4/-2 & mAB = -15/6 \tn % Row Count 16 (+ 1) % Row 7 \SetRowColor{white} M = (5/2, 6) & mAB = 2 & mAB = -5/2 \tn % Row Count 17 (+ 1) % Row 8 \SetRowColor{LightBackground} & C (0, -10) | D (15, 0) & C (-5, 8) | D (10, 14) \tn % Row Count 19 (+ 2) % Row 9 \SetRowColor{white} & mCD = 0 - (-10)/15 - 0 & mCD = 14 - 8/10 - (-5) \tn % Row Count 21 (+ 2) % Row 10 \SetRowColor{LightBackground} & mCD = 10/15 & mCD = 6/15 \tn % Row Count 22 (+ 1) % Row 11 \SetRowColor{white} & mCD = 2/3 & mCD = 2/5 \tn % Row Count 23 (+ 1) % Row 12 \SetRowColor{LightBackground} & ∵ mAB ≠ mCB & 2nd | sub into m1 x m2 = -1 \tn % Row Count 26 (+ 3) % Row 13 \SetRowColor{white} & ∴ not parralell & -5/2 x 2/5 = -1 \tn % Row Count 28 (+ 2) % Row 14 \SetRowColor{LightBackground} & & -10/10 = -1 \tn % Row Count 29 (+ 1) % Row 15 \SetRowColor{white} & & ∴ AB ⊥ CD \tn % Row Count 31 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}---} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}