We appreciate your visit to Select the correct answer from each drop down menu Given tex W 1 1 X 3 4 Y 6 0 tex and tex Z 2. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine if the quadrilateral [tex]$WXYZ$[/tex] is a square, let's check the lengths of its sides and diagonals using the distance formula. If all four sides are equal and both diagonals are equal, then [tex]$WXYZ$[/tex] is a square.
The vertices of the quadrilateral [tex]$WXYZ$[/tex] are given as:
- [tex]\( W(-1, 1) \)[/tex]
- [tex]\( X(3, 4) \)[/tex]
- [tex]\( Y(6, 0) \)[/tex]
- [tex]\( Z(2, -3) \)[/tex]
The distance formula is:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
First, we find the lengths of all four sides [tex]\( WX \)[/tex], [tex]\( XY \)[/tex], [tex]\( YZ \)[/tex], and [tex]\( ZW \)[/tex]:
1. Length of [tex]\( WX \)[/tex]:
[tex]\[
WX = \sqrt{(3 - (-1))^2 + (4 - 1)^2} = \sqrt{(3 + 1)^2 + (4 - 1)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5.0
\][/tex]
2. Length of [tex]\( XY \)[/tex]:
[tex]\[
XY = \sqrt{(6 - 3)^2 + (0 - 4)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5.0
\][/tex]
3. Length of [tex]\( YZ \)[/tex]:
[tex]\[
YZ = \sqrt{(2 - 6)^2 + (-3 - 0)^2} = \sqrt{(-4)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5.0
\][/tex]
4. Length of [tex]\( ZW \)[/tex]:
[tex]\[
ZW = \sqrt{(2 - (-1))^2 + (-3 - 1)^2} = \sqrt{(2 + 1)^2 + (-3 - 1)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5.0
\][/tex]
Now, we need to check the lengths of the diagonals [tex]\( WY \)[/tex] and [tex]\( XZ \)[/tex]:
1. Length of [tex]\( WY \)[/tex]:
[tex]\[
WY = \sqrt{(6 - (-1))^2 + (0 - 1)^2} = \sqrt{(6 + 1)^2 + (0 - 1)^2} = \sqrt{7^2 + (-1)^2} = \sqrt{49 + 1} = \sqrt{50} \approx 7.071
\][/tex]
2. Length of [tex]\( XZ \)[/tex]:
[tex]\[
XZ = \sqrt{(2 - 3)^2 + (-3 - 4)^2} = \sqrt{(2 - 3)^2 + (-3 - 4)^2} = \sqrt{(-1)^2 + (-7)^2} = \sqrt{1 + 49} = \sqrt{50} \approx 7.071
\][/tex]
We have found that:
- All the sides [tex]\( WX \)[/tex], [tex]\( XY \)[/tex], [tex]\( YZ \)[/tex], and [tex]\( ZW \)[/tex] are equal to [tex]\( 5.0 \)[/tex].
- The diagonals [tex]\( WY \)[/tex] and [tex]\( XZ \)[/tex] are equal to approximately [tex]\( 7.071 \)[/tex].
Since all four sides of the quadrilateral are equal and both diagonals are equal, quadrilateral [tex]$WXYZ$[/tex] is a square.
The vertices of the quadrilateral [tex]$WXYZ$[/tex] are given as:
- [tex]\( W(-1, 1) \)[/tex]
- [tex]\( X(3, 4) \)[/tex]
- [tex]\( Y(6, 0) \)[/tex]
- [tex]\( Z(2, -3) \)[/tex]
The distance formula is:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
First, we find the lengths of all four sides [tex]\( WX \)[/tex], [tex]\( XY \)[/tex], [tex]\( YZ \)[/tex], and [tex]\( ZW \)[/tex]:
1. Length of [tex]\( WX \)[/tex]:
[tex]\[
WX = \sqrt{(3 - (-1))^2 + (4 - 1)^2} = \sqrt{(3 + 1)^2 + (4 - 1)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5.0
\][/tex]
2. Length of [tex]\( XY \)[/tex]:
[tex]\[
XY = \sqrt{(6 - 3)^2 + (0 - 4)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5.0
\][/tex]
3. Length of [tex]\( YZ \)[/tex]:
[tex]\[
YZ = \sqrt{(2 - 6)^2 + (-3 - 0)^2} = \sqrt{(-4)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5.0
\][/tex]
4. Length of [tex]\( ZW \)[/tex]:
[tex]\[
ZW = \sqrt{(2 - (-1))^2 + (-3 - 1)^2} = \sqrt{(2 + 1)^2 + (-3 - 1)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5.0
\][/tex]
Now, we need to check the lengths of the diagonals [tex]\( WY \)[/tex] and [tex]\( XZ \)[/tex]:
1. Length of [tex]\( WY \)[/tex]:
[tex]\[
WY = \sqrt{(6 - (-1))^2 + (0 - 1)^2} = \sqrt{(6 + 1)^2 + (0 - 1)^2} = \sqrt{7^2 + (-1)^2} = \sqrt{49 + 1} = \sqrt{50} \approx 7.071
\][/tex]
2. Length of [tex]\( XZ \)[/tex]:
[tex]\[
XZ = \sqrt{(2 - 3)^2 + (-3 - 4)^2} = \sqrt{(2 - 3)^2 + (-3 - 4)^2} = \sqrt{(-1)^2 + (-7)^2} = \sqrt{1 + 49} = \sqrt{50} \approx 7.071
\][/tex]
We have found that:
- All the sides [tex]\( WX \)[/tex], [tex]\( XY \)[/tex], [tex]\( YZ \)[/tex], and [tex]\( ZW \)[/tex] are equal to [tex]\( 5.0 \)[/tex].
- The diagonals [tex]\( WY \)[/tex] and [tex]\( XZ \)[/tex] are equal to approximately [tex]\( 7.071 \)[/tex].
Since all four sides of the quadrilateral are equal and both diagonals are equal, quadrilateral [tex]$WXYZ$[/tex] is a square.
Thanks for taking the time to read Select the correct answer from each drop down menu Given tex W 1 1 X 3 4 Y 6 0 tex and tex Z 2. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
