pls explain?

Question

consider the points a=(-1,2),b=(6,4) and c=(1,-20) in the plane.For how many different points d in the plane are a,b,c,d are the vertices of a parallelogram

Answer 1

3

The points are found opposite the sides of the triangle abc.

To further, if the new points are formed into a bigger triangle the points a,b&c are the midpoints of each side.

Answer 2

yeah 3 is right
Do u know this rule
For a b c d pts forming a parallelogram in that order
ax + cx = bx + dx
ay + cy = by + dy

So, using different arrangements of pts,u will get three possibilites

Say
abcd ..b is opposite to d

bacd........a is opposite to d

bcad ....... c is opposite to d

In first case, using rule stated,
-1 + 1 = 6 + dx
we get dx = -6

2 - 20 = 4 + dy
dy= -22

so d is ( -6,-22)

In this manner u can find 2 other possible points..........

Answer 3

There will be three points in the plane, one in the first quadrant, one in the second and one in the third quadrant for which we can have a parallelogram.