By Alfred Clement Jones
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It II b. Examples Find the equation of a straight line which passes through the origin and makes an angle (i) 45, (ii) 30, (iii) 120, with the axis of x. 1. 2. Draw the straight lines y = I, l t x-\y^ In what points do they intersect ? H. r mul with each other? / the line in each case. r4i/44=0, 3r- 10, = 0, 2y-Kb = Q t 5. Find the equation of the straight line which makes intercepts on the axes twice as long as those made by ly ^x 63. Find the equations of the sides of an equilateral triangle referred to a pair of sides, (ii) to the bisectors of one angle as axes.
12. 4& a y4r 1 = 0, conditions that the straight lines = = a a x4&2y4-c 2 should form an isosceles right-angled 0, a8o:4fe 8t/4c 3 1 triangle, the last line being the hypotenuse. Give, with numerical coefficients, the equations of three such lines. THE EQUATION OF THE FIRST DEGREE ( 55 13. The algebraical sum of the perpendiculars from the points (xl} ;/ t ), X 2> Ui\ ( X ^y^> (#4> I/*) on a straight line is zero show that the line must pass : through the mean centre of the four points. Extend your proof to the case of any n fixed points.
4 Find the equation of the straight line joining the point of intersection of the lines ax + by 4 c c' = to the origin. r-f b'y 0, 12. A square has its centre at the origin one side of the square is the 11. -} : 7 = 0; find the equations of the other three sides. 13. r -f i - ax ' by 4 4
An Introduction to Algebraical Geometry by Alfred Clement Jones