Question 36

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Jambmaths question: 

Find the equation of the straight line through (–2, 3) and perpendicular to 4x +3y – 5 = 0 

Option A: 

$3x+2y-18=0$

Option B: 

$4x+5y+3=0$

Option C: 

$5x-2y-11=0$

Option D: 

$3x-4y+18=0$

Jamb Maths Solution: 

$\begin{align}  & {{l}_{1}}:\text{ }4x+3y-5=0 \\ & \text{      }3y=-4x+5 \\ & \text{       }y=-\tfrac{4}{3}x+\tfrac{5}{3}\text{   (}y=mx+c) \\ & {{m}_{1}}=-\tfrac{4}{3} \\ & \text{For two perpendicular lines} \\ & {{m}_{1}}{{m}_{2}}=-1 \\ & {{m}_{2}}=-\frac{1}{{{m}_{1}}} \\ & {{m}_{2}}=-\frac{1}{-\tfrac{4}{3}}=\frac{3}{4} \\ & \text{Using one}-\text{point form equation for point (}-2,3) \\ & (y-{{y}_{1}})=m(x-{{x}_{1}}) \\ & y-3=\tfrac{3}{4}(x+2) \\ & 4y-12=3x+6 \\ & 3x-4y+18=0 \\\end{align}$

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