Search results for phrase "the coordinates of the vertices of a square are if (3,8) I (15,8) ,J (15,-4) and K (3,-4) what is the lenght of a diagonal of the square ?"

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Search results for phrase "the coordinates of the vertices of a square are if (3,8) I (15,8) ,J (15,-4) and K (3,-4) what is the lenght of a diagonal of the square ?"

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Анонимid Анонимid · Answer 1

Vertices (3, 8) and (15, -4) are opposite vertices connect by a segment to form a diagonal. The diagonals of a square are congruent.

Distance Formula:
D [tex]= \sqrt{(x _{2}-x_{1}) ^{2}+ (y_{2}-y_{1} )^{2} } [/tex]

[tex]x _{1}= 3 [/tex]
[tex]x _{2} =15[/tex]
[tex]y _{1} =8[/tex]
[tex]y_{2} =-4[/tex]

D = [tex] \sqrt{(15-3) ^{2}+(-4-8) ^{2} } [/tex]

D = [tex] \sqrt{(12) ^{2}+(12) ^{2} } [/tex]

D = [tex] \sqrt{144+144} [/tex]

D = [tex] \sqrt{288} [/tex]

D = [tex] \sqrt{(16)(18)} [/tex]

D = [tex]4 \sqrt{(9)(2)} [/tex]

D = [tex](4)(3) \sqrt{2} [/tex]

D = [tex]12 \sqrt{2} [/tex] The length of each diagonal of the square