Question

Is EF and GH parralel and how can this be determined?

Answer 1

We have slope of EF :
`\mathbf{(-4)/(5)}` and slope of GH:
`\mathbf{(-4)/(5)}`

Both have same slope, so EF is parallel to GH i.e. EF || GH

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:
`Slope=(y_2-y_1)/(x_2-x_1)`

Slope of EF

We have: E(2,5) and F(7,1)

So,
`x_1=2, y_1=5, x_2=7, y_2=1`

Putting values in formula and finding slope

`Slope=(y_2-y_1)/(x_2-x_1)\\Slope=(1-5)/(7-2)\\Slope=(-4)/(5)\\`

So, slope of EF is
`\mathbf{(-4)/(5)}`

Slope of GH

We have: G(2,-3) and F(-3,5)

So,
`x_1=2, y_1=-3, x_2=-3, y_2=5`

Putting values in formula and finding slope

`Slope=(y_2-y_1)/(x_2-x_1)\\Slope=(5-(-3))/(-8-2)\\Slope=(5+3)/(-10)\\Slope=(8)/(-10)\\Slope=(-4)/(5)`

So, slope of GH is
`\mathbf{(-4)/(5)}`

We have slope of EF :
`\mathbf{(-4)/(5)}` and slope of GH:
`\mathbf{(-4)/(5)}`

Both have same slope, so EF is parallel to GH i.e. EF || GH