On a coordinate plane, 4 lines are shown. Line A B goes through (negative 4, negative 2) and (4, 2). Line C D goes through (negative 4, 0) and (4, negative 4). Line F G goes through (negative 3, negative 3) and (0, 3). Line H J goes through (negative 1, 3) and (1, negative 1). Which line is perpendicular to a line that has a slope of One-half? line AB line CD line FG line HJ

Answer:The line is HJStep-by-step explanation:we know thatThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] step 1Find the slope line ABwe haveA(-4,-2),B(4,2)substitute the values in the formula[tex]m=\frac{2+2}{4+4}[/tex] [tex]m=\frac{4}{8}[/tex] [tex]m_A_B=\frac{1}{2}[/tex] step 2Find the slope line CDwe haveC(-4,0),D(4,-4)substitute the values in the formula[tex]m=\frac{-4-0}{4+4}[/tex] [tex]m=\frac{-4}{8}[/tex] [tex]m_C_D=-\frac{1}{2}[/tex] step 3Find the slope line FGwe haveF(-3,-3),G(0,3)substitute the values in the formula[tex]m=\frac{3+3}{0+3}[/tex] [tex]m=\frac{6}{3}[/tex] [tex]m_F_G=2[/tex] step 4Find the slope line HJwe haveH(-1,3),J(1,-1)substitute the values in the formula[tex]m=\frac{-1-3}{1+1}[/tex] [tex]m=\frac{-4}{2}[/tex] [tex]m_H_J=-2[/tex] step 5Compare the slopeswe have[tex]m_A_B=\frac{1}{2}[/tex] [tex]m_C_D=-\frac{1}{2}[/tex] [tex]m_F_G=2[/tex] [tex]m_H_J=-2[/tex] we know thatIf two lines are perpendicular, then their slopes are opposite reciprocalsoThe slope of a line perpendicular to a line that has a slope of One-half must be negative 2thereforeThe line is HJ