A parallelogram ABCD has 4 sides with AB parallel to CD and BC parallel to DA. Also, the parallel sides are equal in length.

The slope of the line joining A(-3,2) and B(4,-1) is (2 + 1)/(-3 - 4) = 3/-7

The slope of CD should be -3/7.

Points AB...

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A parallelogram ABCD has 4 sides with AB parallel to CD and BC parallel to DA. Also, the parallel sides are equal in length.

The slope of the line joining A(-3,2) and B(4,-1) is (2 + 1)/(-3 - 4) = 3/-7

The slope of CD should be -3/7.

Points AB are at a distance sqrt((-3-4)^2 + (2+1)^2) = sqrt(49+9) = sqrt 58 from each other. The points C and D have to lie on a line with a slope -3/7 and can be placed anywhere on the line subject to the condition that the distance between them is sqrt 58.

**The required points C and D can be any two points at a distance sqrt 58 from each other and which are on a line with slope -3/7. **