Theory question 111
Coordinate Geometry(a) Find the equation of the line that passes through the origin and the point of intersection of the lines x + 2y = 7 and x − y = 4.
(b) The ratio of an interior angle to an exterior angle of a regular polygon is 4:1. Find the: (i) number of sides; (ii) value of the exterior angle; (iii) sum of the interior angles of the polygon.
Show the model answer
Model answer
(a) Subtracting: 3y = 3 ⇒ y = 1, x = 5; the line through (0, 0) and (5, 1) is y = x/5 (5y = x)
(b) Interior + exterior = 180° and interior = 4 × exterior ⇒ exterior = 36°
(i) Number of sides = 360° ÷ 36° = 10
(ii) Exterior angle = 36°
(iii) Sum of interior angles = (10 − 2) × 180° = 1440°
Explanation
A line through the origin has equation y = mx.