The length of lines UV, VW, WX, and UX are: = √65 units, 10 units,√65 units and 10 units respectively.
<h3>What is Distance Formula?</h3>
Algebraic expression that gives the distances between pairs of points in terms of their coordinates
Given that: U(7,9), V(0,5), W(-6,-3) ,X(1,1)
The length can be find by using Distance Formula,
Length of UV,
= ![\sqrt{(0-7)^{2} + (5-9)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%280-7%29%5E%7B2%7D%20%2B%20%285-9%29%5E%7B2%7D%7D)
= ![\sqrt{49+16}](https://tex.z-dn.net/?f=%5Csqrt%7B49%2B16%7D)
= √65 units
Length of VW,
= ![\sqrt{(-6-0)^{2}+(-3-5)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-6-0%29%5E%7B2%7D%2B%28-3-5%29%5E%7B2%7D%7D)
= ![\sqrt{36 + 64}](https://tex.z-dn.net/?f=%5Csqrt%7B36%20%2B%2064%7D)
=√100 units
= 10 units
Length of WX,
=![\sqrt{(1-(-6))^{2}+(1-(-3))^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%281-%28-6%29%29%5E%7B2%7D%2B%281-%28-3%29%29%5E%7B2%7D%7D)
= √49+ 14
= √65 units
Length of XU,
= ![\sqrt{(7-1)^{2}+(9-1)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%287-1%29%5E%7B2%7D%2B%289-1%29%5E%7B2%7D%7D)
= √36+64
=√100 units
= 10 units
Length of UW,
= ![\sqrt{(-6-7)^{2}+(-3-9)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-6-7%29%5E%7B2%7D%2B%28-3-9%29%5E%7B2%7D%7D)
= √169+144
=√313 units
Length of VX,
= ![\sqrt{(1-0)^{2}+(5-1)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%281-0%29%5E%7B2%7D%2B%285-1%29%5E%7B2%7D%7D)
= √1+16
=√17 units
Thus, Length of opposite sides are equal but the length of diagonals are not Equal. So, the quadrilateral is a parallelogram.
Learn more about distance formula here:
brainly.com/question/12674171
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