Question

The coordinates of the endpoints of and are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which condition proves that ?

Answer 1

the complete question in the attached figure

we know that

Two lines are parallel if they have the same slope.

So

Computing for the slope of line segment AB and line segment CD using the formula

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

step 1

Find the slope segment AB

`A(x1, y1), B(x2, y2)`

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

step 2

Find the slope segment CD

`C(x3, y3), D(x4, y4)`

`mCD=((y4-y3))/((x4-x3))`

step 3

If AB is parallel to CD

then

`mAB=mCD`

`((y2-y1))/((x2-x1))=((y4-y3))/((x4-x3))`

therefore

the answer is

`((y2-y1))/((x2-x1))=((y4-y3))/((x4-x3))`

Answer 2

for two line segments to be parallel, their slopes must be equal.

Therefore slope of AB must be equal to slope of CD

which is, option 3
(y4-y3)/(x4-x3)=(y2-y1)/(x2-x1)