Question

Please help with this question!!

Answer 1

`\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\\\\l\perp k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\\text{We have the points J(-24, -4) and K(-4, 6)}.\\\\\text{The formula of a slope:}\\\\m=(y_2-y_1)/(x_2-x_1)\\\\\text{substitute:}\\\\m_1=(6-(-4))/(-4-(-24))=(10)/(20)=(1)/(2)\\\\\text{therefore}\ m_2=-(1)/((1)/(2))=-2\\\\\text{The formula of a midpoint:}\\\\\left((x_1+x_2)/(2);\ (y_1+y_2)/(2)\right)\\\\\text{substitute the coordinates of the points J and K:}`

`x=(-24+(-4))/(2)=(-28)/(2)=-14\\\\y=(-4+6)/(2)=(2)/(2)=1\\\\\text{midpoint}\ (-14,\ 1)\\\\\text{The point-slope form:}\\\\y-y_1=m(x-x_1)\\\\\text{substitute}\ m=-2,\ x_1=-14\ \text{and}\ y_1=1:\\\\y-1=-2(x-(-14))\\\\\boxed{y-1=-2(x+14)}`