A rectangle is drawn on a coordinate grid. The equation for one side of the rectangle is 2x – 5y = 9. Which could be the equation of another side of the rectangle?

Answer:[tex]25x+10y+18=0[/tex]Step-by-step explanation:We are given that a rectangle in which the equation of one side is given by [tex]2x-5y=9[/tex]We have to find the equation of another side of the rectangle.We know that the adjacent sides of rectangle are perpendicular to each other.Differentiate the given equation w.r.t.x[tex]2-5\frac{dy}{dx}=0[/tex]   ([tex]\frac{dx^n}{dx}=nx^{n-1}[/tex])[tex]5\frac{dy}{dx}=2[/tex][tex]\frac{dy}{dx}=\frac{2}{5}[/tex]Slope of the given side=[tex]m_1=\frac{2}{5}[/tex]When two lines are perpendicular then Slope of one line=[tex]-\frac{1}{Slope\;of\;another\;line}[/tex]Slope of another side=[tex]-\frac{5}{2}[/tex]Substitute x=0 in given equation [tex]2(0)-5y=9[/tex][tex]-5y=9[/tex][tex]y=-\frac{9}{5}[/tex]The equation of given side is passing through the point ([tex]0,-\frac{9}{5})[/tex].The equation of line passing through the point [tex](x_1,y_1)[/tex] with slope m is given by [tex]y-y_1=m(x-x_1)[/tex]Substitute the values then we get [tex]y+\frac{9}{5}=-\frac{5}{2}(x-0)=-\frac{5}{2}x[/tex][tex]y=-\frac{5}{2}x-\frac{9}{5}[/tex][tex]y=\frac{-25x-18}{10}[/tex][tex]10y=-25x-18[/tex][tex]25x+10y+18=0[/tex]Hence, the equation of another side of rectangle is given by [tex]25x+10y+18=0[/tex]