Find the distance between the pair of parallel lines.y = 2x + 4y = 2x – 4A) 4.01B) 3.84C) 3.58D) 3.65

Answer:C) 3.58Step-by-step explanation:The distance between two parallel lines r1 and r2 is given by the absolute value of:[tex]d(r_1,r_2)=\frac{ax_1+by_1+c}{\sqrt{a^{2}+b^{2}}}[/tex]Where a, b and c are the coefficients of the general form of the equation of the line r2 and x1 and y2 are the coordinates of one point that belongs to the line r1.Let's call r1 the line define by: y = 2x +4 and r2 the line define by y=2x-4So, the general form of the equation of line r2 is:y = 2x - 40 = 2x - 4 - y0 = 2x - y - 4With this equation, a is equal to 2, b is equal to -1 and c is equal to -4.Now, we need to found a point that belongs to line r1. This point can be found replacing x for any value and found y. If x is cero, for example, y is:y = 2x +4y = 2*0 + 4y = 4So, our point (x1, y1) is (0,4). Replacing values of the equation of d(r1,r2), we get:[tex]d(r_1,r_2)=\frac{(2*0)+(-1*4)+(-4)}{\sqrt{2^{2}+(-1)^{2}}}=[/tex][tex]d(r_1,r_2)=\frac{-8}{\sqrt{5}} = -3.58[/tex]Then, the absolute value of -3.58 is 3.58, so the distance between the two parallel lines is 3.58.