Question 27977: could you please help me.
DIRECTIONS:
determine whether the given vertices represent a parallelogram,rectangle,rhombus,or square.explain your reasoning.
A(-3,0)B(-1,3)C(5,-1)D(3,-4)
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! determine whether the given vertices represent a parallelogram,rectangle,rhombus,or square.explain your reasoning.
A(-3,0)B(-1,3)C(5,-1)D(3,-4)
I TEST....DIAGONALS BISECT OR NOT ?
MID POINT OF AC =(-3+5)/2,(0-1)/2=(1,-1/2)
MID POINT OF BD =(-1+3)/2,(3-4)/2=(1,-1/2)...SAME.....
SO DIAGONALS BISECT.HENCE IT IS A parallelogram,rectangle,rhombus,or square
II TEST......ADJACENT SIDES ARE AT RIGHT ANGLE?
SLOPE OF AB =(3-0)/(-1+3)=3/2
SLOPE OF BC = (-1-3)/(5+1)=-4/6=-2/3
PRODUCT OF SLOPES = (3/2)*(-2/3)=-1....HENCE THEY INTERSECT AT RIGHT ANGLE.
HENCE IT IS A RECTANGLE OR SQUARE.
III TEST......DIAGONALS ARE AT RIGHT ANGLE ?
SLOPE OF AC = (-1-0)/(5+3)=-1/8
SLOPE OF BD = (-4-3)/(3+1)=-7/4
PRODUCT OF SLOPES IS NOT -1.HENCE THEY ARE NOT AT RIGHT ANGLE
HENCE IT IS A RECTANGLE.
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