How could you use coordinate geometry to prove that BC || AD?
Prove the slopes are the same
Prove the slopes are opposite reciprocals
Prove the lengths are the same
Prove the midpoints are the same

The correct answer could be "Prove the slopes are the same" or "Prove the lengths are the same" (Length of opposite sides of ABCD). Option 1 and 3 can be correct.

Given information:

A quadrilateral ABCD is given in the figure and it is asked to prove that the line BC is parallel to AD.

Now, in a quadrilateral, if the pair of opposite sides are equal, then the quadrilateral is a parallelogram.

So, from this definition of parallelogram, The opposite sides will be parallel or simply BC || AD.

Now, one more concept can be used here. The lines with same slope will make same angle with the x-axis and hence, they will be parallel.

So, if the slope of line BC and AD is equal, then the lines will be parallel.

Therefore, the correct answer could be "Prove the slopes are the same" or "Prove the lengths are the same" (Length of opposite sides). Option 1 and 3 can be correct.

NOTE: if the question has only one correct option, then option 1 will be correct.

For more details, refer to the link:

link

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: