Answer:
We have slope of EF : [tex]\mathbf{\frac{-4}{5}}[/tex] and slope of GH: [tex]\mathbf{\frac{-4}{5}}[/tex]
Both have same slope, so EF is parallel to GH i.e. EF || GH
Step-by-step explanation:
We need to find Is EF and GH parallel.
If EF and GH are parallel, they have same slopes.
So, we will find slopes of EF and GH
The formula used is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of EF
We have: E(2,5) and F(7,1)
So, [tex]x_1=2, y_1=5, x_2=7, y_2=1[/tex]
Putting values in formula and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{1-5}{7-2}\\Slope=\frac{-4}{5}\\[/tex]
So, slope of EF is [tex]\mathbf{\frac{-4}{5}}[/tex]
Slope of GH
We have: G(2,-3) and F(-3,5)
So, [tex]x_1=2, y_1=-3, x_2=-3, y_2=5[/tex]
Putting values in formula and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{5-(-3)}{-8-2}\\Slope=\frac{5+3}{-10}\\Slope=\frac{8}{-10}\\Slope=\frac{-4}{5}[/tex]
So, slope of GH is [tex]\mathbf{\frac{-4}{5}}[/tex]
We have slope of EF : [tex]\mathbf{\frac{-4}{5}}[/tex] and slope of GH: [tex]\mathbf{\frac{-4}{5}}[/tex]
Both have same slope, so EF is parallel to GH i.e. EF || GH
