Answer:
1. Neither
2. 1 over 7
Step-by-step explanation:
We know that the formula for slope joining the points \(( x_{1} ,y_{1} )\) and \(( x_{2} ,y_{2} )\) is given by \(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\).
1. We have the line FG having end points ( 3,7 ) and ( -4,-5 ). The slope of this line is given by,
\(m_{FG}=\frac{-5-7}{-4-3}\)
i.e. \(m_{FG}=\frac{-12}{-7}\)
i.e. \(m_{FG}=1.714\)
Also, the line HI is given with end points ( -1,0 ) and ( 4,6 ). Its slope is given by,
\(m_{HI}=\frac{6-0}{4+1}\)
i.e. \(m_{HI}=\frac{6}{5}\)
i.e. \(m_{HI}=1.2\)
Since, neither the slope of FG and HI are equal nor their product is -1.
Hence, FG and HI are neither parallel nor perpendicular respectively.
2. We have the line AB with end points ( 8,-4 ) and ( 1,-5 ). So, the slope of AB is,
\(m_{AB}=\frac{-5+4}{1-8}\)
i.e. \(m_{AB}=\frac{-1}{-7}\)
i.e. \(m_{AB}=\frac{1}{7}\)
Hence, slope of AB is 1 over 7.
