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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 ?

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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 ? Please Look A Picture For A Better Loo class=

Verified Answer :

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)

Answer with explanation:

When two lines are parallel, then their slopes are equal.

It is given that, AB ║ CD.

Coordinates of A, B, C and D are,

        \(A(x_{1}, y_{1}), B(x_{2}, y_{2}), C(x_{3}, y_{3}), and D(x_{4}, y_{4})\)

→→Slope of AB=Slope of CD

\(\rightarrow\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y_{4}-y_{3}}{x_{4}-x_{3}}\)

Option : C

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