The length of lines UV, VW, WX, and UX are: = √65 units, 10 units,√65 units and 10 units respectively.
What is Distance Formula?
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,
= [tex]\sqrt{(0-7)^{2} + (5-9)^{2}}[/tex]
= [tex]\sqrt{49+16}[/tex]
= √65 units
Length of VW,
= [tex]\sqrt{(-6-0)^{2}+(-3-5)^{2}}[/tex]
= [tex]\sqrt{36 + 64}[/tex]
=√100 units
= 10 units
Length of WX,
=[tex]\sqrt{(1-(-6))^{2}+(1-(-3))^{2}}[/tex]
= √49+ 14
= √65 units
Length of XU,
= [tex]\sqrt{(7-1)^{2}+(9-1)^{2}}[/tex]
= √36+64
=√100 units
= 10 units
Length of UW,
= [tex]\sqrt{(-6-7)^{2}+(-3-9)^{2}}[/tex]
= √169+144
=√313 units
Length of VX,
= [tex]\sqrt{(1-0)^{2}+(5-1)^{2}}[/tex]
= √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.
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