Question

Ignore the stuff around it ,could someone explain me this?

Answer 1

The lines blue and green are perpendicular

Explanation:

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

step 1

Find the slope of the blue line

we have the points

(-1,-3) and (0,3)

substitute

`m=(3+3)/(0+1)`

`m=(6)/(1)=6`

step 2

Find the slope of the red line

we have the points

(3,-3) and (4,2)

substitute

`m=(2+3)/(4-3)`

`m=(5)/(1)=5`

step 3

Find the slope of the green line

we have the points

(-4,-1) and (2,-2)

substitute

`m=(-2+1)/(2+4)`

`m=-(1)/(6)`

step 4

Compare the slopes

Blue line ---->
`m=6`

Red line ----.
`m=5`

Green line --->
`m=-(1)/(6)`

so

The slope of the blue line and the green line are opposite reciprocal ( their product is equal to -1)

therefore

The lines blue and green are perpendicular