Question

are the following perpendicular, parallel or neither? How do you know? a) 9x-12y=17 and 3x-4y= 17 b) 5x+6y=30 and 6x+5y=24

Answer 1

We know that two lines angle between them is oo & if angle between them is are are 90o. parallel if perpendiculer If y=mx+c & Y= m₂ x tc are two lines having slope m, & m₂ then angle blo them is out 5m, - m2] o= tan Litm, m₂ or tano =- m - m2 - (*) tm, m2 Now if lines are parallel then o=0 1.e. tan o= m,-mz. Itm, mz o m, m2 tm, m2 m, - m₂=0 m = m₂]

and if lines are perpendicular m.-m2 ic 0-90° then tango = tm, mz o = m m₂ m, m2 It m, mz 1+m, m2=0 mm, =-17 (a) Given lines are 9x-12y = 17 2 lin slope - intercept form 32-44 =17 77 9x-124 =17 I 12y = 92 -17 3 line 37-44 =17 in slope intercept / y = 1 / 2 x - 1/2 comparing form becomes I with y = mxtc. 44= 3x-17 y = 3x - 1 I comparing mi = 2 2 2 = 3 - 5 with y = m₂ x + C2 we get m₂ = 3/4 3 since m = 3 = m₂ i.e. m = m₂) so lines are parallel. (6) Given lines are = 5% +67 = 30 & 6x + 5y = 23 24 writing in slope intercept form - by = -5x+30 & 54-6x +30 y = -5x +30 ; y = - 6x + 24 Comparing with y = m, xtc, & y = m₂ x+ we have m, - - f m = -6 We see im neither m = m, nor mm = -1 holds. as mm, --1-97 so given lines are neither parallel nor perpendicular. These lines are inclined at some angle which can be evaluated by formula (*).