The points (5$$, $$-$$ $$4$$,$$2),(4$$,$$-$$ $$3$$, $$1),(7$$, $$-$$ $$6$$, $$4) and (8$$, $$-$$ $$7$$ , $$5) are the vertices of

Question

Infinity Learn · Accepted Answer

Let , $$A(5$$, $$-4$$,$$2)$$, $$B(4$$, $$-$$ $$3$$, $$1)$$, $$C(7$$, $$-6$$, $$4)$$ and $$D(8$$, $$-$$ $$7$$ ,$$5)$$. Then,$$AB=(4$$−$$5)2+($$−$$3+4)2+(1$$−$$2)2=1+1+1=3BC=(7$$−$$4)2+($$−$$6+3)2+(4$$−$$1)2=9+9+9=33CD=(8$$−$$7)2+($$−$$7+6)2+(5$$−$$4)2=1+1+1=3AD=(8$$−$$5)2+($$−$$7+4)2+(5$$−$$2)2=9+9+9=33AC=(7$$−$$5)2+($$−$$6+4)2+(4$$−$$2)2=4+4+4=23BD=(8$$−$$4)2+($$−$$7+3)2+(5$$−$$1)2=16+16+16=43Here$$, we see that opposite sides .AB $$=$$ CD,BC $$=$$ AD are equal and diagonals AC≠BDHence, given points are the vertices of a parallelogram.

The points (5, - 4,2),(4,- 3, 1),(7, - 6, 4) and (8, - 7 , 5) are the vertices of

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