Help Please

can you walk me through these questions, there pretty confusing...

7. Verify that Parallelogram ABCD with vertices A(-5,-1), B(-9,6), C(-1,5), and D(3,-2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals

8. if you were to place a rhombus in the coordinate plane so that its diagonals lie along the axes, what would be the coordinates of the vertices using as few variables as possible

Question

Help Please 

can you walk me through these questions, there pretty confusing...

7. Verify that Parallelogram ABCD with vertices A(-5,-1), B(-9,6), C(-1,5), and D(3,-2) is a rhombus by showing that it is a parallelogram with perpendicular diagonals 

8. if you were to place a rhombus in the coordinate plane so that its diagonals lie along the axes, what would be the coordinates of the vertices using as few variables as possible

calculusfunctions · Answer

If the diagonals are perpendicular, then their slopes must be negative reciprocals.

calculusfunctions · Answer

For the second one, just think. If the diagonals are placed on the coordinate axes, then the vertices must also be on the coordinate axes. Remember diagonals are line segments between opposite vertices.

anonymous · Answer

@calculusfunctions don't I have to solve something?

zpupster · Answer

you can calculate the slopes
y2-y1/x2-x1= slope

Say Aand C is opposite
5-(-1)/-1-(-5) = 5+1/-1+5 = 6/4 or 3/2

do it for B and and see if the slopes are negative reciprocals