MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane
Problem
Five straight lines are given below.
L1:y=3x−4L2:2y=6x+1L3:x=5L4:y=2L5:3x+y=7
(i) Rewrite each equation (where possible) in slope–intercept form and state the slope of every line. For any line whose slope is not defined, mention that explicitly.
(ii) List all distinct pairs of lines that are parallel. Justify your answer using the slopes found in part (i).
(iii) List all distinct pairs of lines that are perpendicular. Justify your answer using the slopes found in part (i).
(iv) The lines L1 and L3 intersect at the point P. Determine the coordinates of P, and write the equation of the line that passes through P and is perpendicular to L1.