whuch sides of a triangle ABC are equal if the coordinates of vertices are A(1,5) B(3,1) c(-3,3)?
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whuch sides of a triangle ABC are equal if the coordinates of vertices are A(1,5) B(3,1) c(-3,3)?
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[tex] d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
From A(1, 5) to B(3,1)
[tex] d=\sqrt{(3-1)^{2}+(1-5)^{2} } \\= \sqrt{(2)^{2}+(-4)^{2}} \\ \sqrt{4+16} \\=\sqrt{20}\\= 4.472135955 [/tex]
[tex] [/tex]
From B(3,1) to C(-3,3)
[tex] d=\sqrt{((-3)-3)^{2}+(3-1)^{2} } \\= \sqrt{(-6)^{2}+(2)^{2}} \\ \sqrt{36+4} \\=\sqrt{40}\\= 6.3245553203 [/tex]
[tex] [/tex]
From C(-3,3) to A(1,5)
[tex] d = \sqrt{ (1-(-3))^{2}+(5-3)^{2} } \\= \sqrt{ (4)^{2}+(2)^{2} } \\ \sqrt{16+4} \\ = \sqrt{20} \\= 4.472135955 [/tex]
[tex] [/tex]
Therefore, [tex] \overline{AB}\: \text{and}\: \overline{CA} [/tex] are EQUAL.