Answer :
Draw an accurate picture of the trapezoid.
The parallel bases are clearly DC and AB.
The Distance formula between 2 points P(a, b) and Q(c, d) states that:
[tex]|PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2} } [/tex]
Using this formula we find:
[tex]|AB|= \sqrt{ (0-3)^{2} + (5-3)^{2} }=\sqrt{ 9+4}= \sqrt{ 13}[/tex]
[tex]|CD|= \sqrt{ (5-(-1))^{2} + (-2-2)^{2} }=\sqrt{ 36+16}=\sqrt{52}=2\sqrt{13}=[/tex]
The length of the midsegment of a trapezoid is
[tex] \frac{|base_1|+|base_2|}{2}= \frac{\sqrt{ 13}+2\sqrt{ 13}}{2}= \frac{3\sqrt{13}}{2}[/tex]
Answer: [tex]\frac{3\sqrt{13}}{2}[/tex]
The parallel bases are clearly DC and AB.
The Distance formula between 2 points P(a, b) and Q(c, d) states that:
[tex]|PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2} } [/tex]
Using this formula we find:
[tex]|AB|= \sqrt{ (0-3)^{2} + (5-3)^{2} }=\sqrt{ 9+4}= \sqrt{ 13}[/tex]
[tex]|CD|= \sqrt{ (5-(-1))^{2} + (-2-2)^{2} }=\sqrt{ 36+16}=\sqrt{52}=2\sqrt{13}=[/tex]
The length of the midsegment of a trapezoid is
[tex] \frac{|base_1|+|base_2|}{2}= \frac{\sqrt{ 13}+2\sqrt{ 13}}{2}= \frac{3\sqrt{13}}{2}[/tex]
Answer: [tex]\frac{3\sqrt{13}}{2}[/tex]
