A point is said to be equidistant from the two coordinate axes when its perpendicular distance from the x-axis equals that from the y-axis. Answer the questions below.
(i) Derive the relation that the coordinates (x,y) of such a point must satisfy.
(ii) Using the relation obtained in part (i), find two possible coordinates of points whose abscissa is −6 and which are equidistant from both axes.
(iii) A point lies in the second quadrant and is 7 units away from each axis. Determine its coordinates and explain why your answer satisfies all the conditions.
(iv) Show that all points equidistant from both axes lie on two straight lines. Write the equations of these lines and explain how they follow from part (i).