Answer:
XZ = XY = 5 units are equal .
ΔXYZ is a Right isosceles triangle .
Step-by-step explanation:
As to an triangle is isosceles triangles the two sides of the triangle must be equal .
Formula
[tex]Distance\ formula = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
As the vertices of the ΔXYZ be X (1,3) , Y (4,-1) and Z(5,6) .
[tex]XY = \sqrt{(4-1)^{2}+(-1-3)^{2}}[/tex]
[tex]XY = \sqrt{(3)^{2}+(-4)^{2}}[/tex]
[tex]XY = \sqrt{9+16}[/tex]
[tex]XY = \sqrt{25}[/tex]
[tex]\sqrt{25}= 5[/tex]
[tex]XY = 5\ units[/tex]
[tex]YZ = \sqrt{(5-4)^{2}+(6-(-1))^{2}}[/tex]
[tex]YZ = \sqrt{(1)^{2}+(7)^{2}}[/tex]
[tex]YZ = \sqrt{1+49}[/tex]
[tex]YZ = \sqrt{50}\ units[/tex]
[tex]ZX = \sqrt{(1-5)^{2}+(3-6)^{2}}[/tex]
[tex]ZX = \sqrt{(-4)^{2}+(-3)^{2}}[/tex]
[tex]ZX = \sqrt{16+9}[/tex]
[tex]ZX = \sqrt{25}[/tex]
[tex]\sqrt{25}= 5[/tex]
ZX = 5 units
Thus XZ = XY = 5 units are equal .
Therefore ΔXYZ is a Right isosceles triangle .
