For quadrilateral ABCD, the coordinates of vertices A and B are A(1,2) and B(2,-2). Match each set of coordinates for vertices C and D, that is the most specific way to classify the quadrilateral.?

C(-6,-4), D(-7,0)

C(6,-1), D(5,3)

C(-1,-4), D(-2,0)

C(1,-6), D(0,-2)

Answer 1

A - Rectangle B - Square
C - Parallelogram D - Rhombus

We are given #A(1,2), B(2,-2)# and hence #AB=sqrt((2-1)^2+(-2-2)^2)=sqrt17#. Further slope of #AB# is #(-2-2)/(2-1)=-4/1=-4#.
Case A - #C(-6,-4), D(-7,0)#
As #CD=sqrt((-7-(-6))^2+(0-(-4))^2)=sqrt17# and slope of #CD# is #(0-(-4))/(-7-(-6))=4/(-1)=-4#
As #AB=CD# and #AB#||#CD# slopes being equal, ABCD is a parallelogram. graph{((x-1)^2+(y-2)^2-0.08)((x-2)^2+(y+2)^2-0.08)((x+6)^2+(y+4)^2-0.08)((x+7)^2+y^2-0.08)=0 [-10, 10, -5, 5]}
Case B - #C(6,-1), D(5,3)#
As #CD=sqrt((5-6)^2+(3-(-1))^2)=sqrt17# and slope of #CD# is #(0-(-4))/(-7-(-6))=4/(-1)=-4#
Further, #BC=sqrt((6-2)^2+(-1-(-2))^2)=sqrt17# and slope of #BC# is #(-1-(-2))/(6-2)=1/4#
As #BC=AB# and they are perpendicular (as product of slopes is #-1#), ABCD is a square. graph{((x-1)^2+(y-2)^2-0.08)((x-2)^2+(y+2)^2-0.08)((x-6)^2+(y+1)^2-0.08)((x-5)^2+(y-3)^2-0.08)=0 [-10, 10, -5, 5]}
Case C - #C(-1,-4), D(-2,0)#
As mid point of #AC# is #((1-1)/2,(2-4)/2)# i.e. #(0,-1)# and midpoint of #BD# is #((2-2)/2,(-2+0)/2# i.e. #(0,-1)# i.e. midpoints of #AC# and #BD# are same,
but, #BC=sqrt((2-(-1))^2+(-2-(-4))^2)=sqrt13# i.e. #AB!=BC# and hence ABCD is a parallelogram. graph{((x-1)^2+(y-2)^2-0.08)((x-2)^2+(y+2)^2-0.08)((x+1)^2+(y+4)^2-0.08)((x+2)^2+y^2-0.08)=0 [-10, 10, -5, 5]}
Case D - #C(1,-6), D(0,-2)#
As mid point of #AC# is #((1+1)/2,(2-6)/2)# i.e. #(1,-2)# and midpoint of #BD# is #((2+0)/2,(-2+(-2))/2# i.e. #(1,-2)# i.e. midpoints of #AC# and #BD# are same,
and, #BC=sqrt((2-1)^2+(-2-(-6))^2)=sqrt17# i.e. #AB=BC# and hence ABCD is a rhombus. graph{((x-1)^2+(y-2)^2-0.08)((x-2)^2+(y+2)^2-0.08)((x-1)^2+(y+6)^2-0.08)(x^2+(y+2)^2-0.08)=0 [-14, 14, -7, 7]}
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To classify the quadrilateral formed by vertices A(1,2) and B(2,-2) based on the coordinates of vertices C and D, we need to consider various possibilities:

  1. If the coordinates of vertices C and D are such that the quadrilateral has opposite sides parallel and equal in length, it is a parallelogram. Possible coordinates for C and D in this case could be C(1,5) and D(2,9).

  2. If the coordinates of vertices C and D are such that one pair of opposite sides is parallel and equal in length, and the other pair of opposite sides is not parallel, it is a trapezoid. Possible coordinates for C and D in this case could be C(4,2) and D(5,4).

  3. If the coordinates of vertices C and D are such that all sides are equal in length and all angles are right angles, it is a rectangle. Possible coordinates for C and D in this case could be C(1,-2) and D(4,-2).

  4. If the coordinates of vertices C and D are such that all sides are equal in length but not all angles are right angles, it is a rhombus. Possible coordinates for C and D in this case could be C(3,2) and D(4,5).

  5. If the coordinates of vertices C and D are such that the diagonals are perpendicular and bisect each other, it is a kite. Possible coordinates for C and D in this case could be C(3,-2) and D(4,-3).

Therefore, based on the coordinates of vertices C and D, we can classify the quadrilateral in the most specific way as either a parallelogram, trapezoid, rectangle, rhombus, or kite.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7