Moderate -0.8 This is a straightforward coordinate geometry question requiring two standard techniques: finding the perpendicular gradient (negative reciprocal of 4 is -1/4) and using point-slope form to find the equation, then setting y=0 to find the x-intercept. All steps are routine applications of basic formulas with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature.
\includegraphics{figure_7}
The line AB has equation \(y = 4x - 5\) and passes through the point B(2, 3), as shown in Fig. 7. The line BC is perpendicular to AB and cuts the \(x\)-axis at C. Find the equation of the line BC and the \(x\)-coordinate of C. [5]
\includegraphics{figure_7}
The line AB has equation $y = 4x - 5$ and passes through the point B(2, 3), as shown in Fig. 7. The line BC is perpendicular to AB and cuts the $x$-axis at C. Find the equation of the line BC and the $x$-coordinate of C. [5]
\hfill \mbox{\textit{OCR MEI C1 2006 Q7 [5]}}