+50 If lines \( y=(2a-5)x-5\) and \(9y=(a+2)x-3\) are perpendicular, what are all the possible values of \(a\)? Express your answers in decreasing order, separated by commas.
+118609 Dear thisismyname,
I know that this is a repeat question. That is fine but next time could you please put a link to the old question so that there is no chance of it being answered twice :)
If I can easily find your first question - I will delete it :)
If lines $y=(2a-5)x-5$ and $9y=(a+2)x-3$ are perpendicular, what are all the possible values of ? Express your answers in decreasing order, separated by commas.
If 2 lines are perpendicular the product of the gradients MUST equal -1
or to put it another way,
One gradient is the negative reciprocal of the other. (except if one gradient is 0 and the other is infinity )
\(y=(2a-5)x-5 \quad (1)\\ y=\frac{a+2}{9}\;x-\frac{3}{9} \qquad (2)\\ (2a-5)* \frac{a+2}{9}=-1\\ (2a-5)* (a+2)=-9\\ 2a^2+4a-5a-10=-9\\ 2a^2-a-1=0\\ 2a^2-2a+a-1=0\\ 2a(a-1)+1(a-1)=0\\ (2a+1)(a-1)=0\\ a=-0.5\;\;a=1\\ solution\\ 1,\;-0.5\)
