Crystal is writing a coordinate proof to show that the diagonals of a parallelogram bisect each other. she starts by assigning coordinates as given.

We can fill all the boxes with help of below explanation.

Explanation:

Since here, ABCD is a parallelogram with vertices A, B, C and D and diagonals AC and BD.

Where, it is given A≡(0,0), B≡(a,0) and D≡(b,c)

According to the given figure,

The coordinates of C are (a+b, c) ( since, Both points C and D are equally far from X-axis therefore, they both have same y-coordinate.)

Now, again from the diagram, E is the midpoint of both Diagonals BD and AC.

where, coordinates of E are

Thus, by the definition of midpoints and .

Also, BD and AC are intersecting at point E.

Therefore AC and BD bisect each other.

search the worksheet up on the internet

step-by-step explanation:

it works trust me

where's the diagram?

step-by-step explanation: