Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Select the correct answer from each drop-down menu.

A quadrilateral has vertices [tex][tex]$A(11,-7), B(9,-4), C(11,-1)$[/tex][/tex], and [tex][tex]$D(13,-4)$[/tex][/tex].
Quadrilateral [tex][tex]$ABCD$[/tex][/tex] is a [tex][tex]$\square$[/tex][/tex].

If the vertex [tex][tex]$C(11,-1)$[/tex][/tex] were shifted to the point [tex][tex]$C^{\prime}(11,1)$[/tex][/tex], quadrilateral [tex][tex]$ABC^{\prime}D$[/tex][/tex] would be a [tex][tex]$\square$[/tex][/tex].

Sagot :

GinnyAnswer
To determine the type of quadrilaterals, we need to examine the relationships between the sides and diagonals of quadrilateral [tex]\(ABCD\)[/tex] with vertices [tex]\( A(11, -7) \)[/tex], [tex]\( B(9, -4) \)[/tex], [tex]\( C(11, -1) \)[/tex], and [tex]\( D(13, -4) \)[/tex] and the modified quadrilateral [tex]\(ABCD'\)[/tex] where [tex]\( C'(11, 1) \)[/tex].

### Step 1: Check properties of Quadrilateral [tex]\(ABCD\)[/tex]
First, let's determine if quadrilateral [tex]\(ABCD\)[/tex] is a parallelogram, rectangle, or some other quadrilateral.

The primary properties we look for are:
- Opposite sides being equal for a parallelogram.
- Both the above property and the diagonals being equal for a rectangle.

Since we have calculated earlier, quadrilateral [tex]\(ABCD\)[/tex] satisfies neither of these properties (it is neither a parallelogram nor a rectangle).

### Conclusion for Quadrilateral [tex]\(ABCD\)[/tex]
Quadrilateral [tex]\(ABCD\)[/tex] is neither a parallelogram nor a rectangle.

### Step 2: Check properties of Quadrilateral [tex]\(ABC'D\)[/tex]
Now, shift vertex [tex]\(C\)[/tex] to [tex]\(C'(11, 1)\)[/tex] and form quadrilateral [tex]\(ABC'D\)[/tex]. Again, we need to check the properties:
- Opposite sides being equal for a parallelogram.
- Both the above property and the diagonals being equal for a rectangle.

From our calculations, quadrilateral [tex]\(ABC'D\)[/tex] also satisfies neither of these properties (it is neither a parallelogram nor a rectangle).

### Conclusion for Quadrilateral [tex]\(ABC'D\)[/tex]
Quadrilateral [tex]\(ABC'D\)[/tex] is neither a parallelogram nor a rectangle.

### Final Answer:
Quadrilateral [tex]\(ABCD\)[/tex] is a _general quadrilateral_ (not specifically a parallelogram or rectangle). Quadrilateral [tex]\(ABC'D\)[/tex] is also a _general quadrilateral_ (not specifically a parallelogram or rectangle).
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.