Respuesta :
The triangle is an isosceles triangle with sides XY and XZ equal to [tex]\sqrt{29}[/tex] units and side YZ as 4 units.
Given that:-
Coordinates of X = (7,6)
Coordinates of Y = (5,1)
Coordinates of Z = (9,1)
We have to find the measures of the sides of ΔXYZ and classify the triangle by its sides.
Using distance formula, we can find the measure of the sides of the triangle.
Distance formula for the line segment with points (a,b) and (c,d):-
[tex]\sqrt{(d-b)^2+(c-a)^2}[/tex]
Hence,
XY = [tex]\sqrt{(1-6)^2+(5-7)^2} =\sqrt{25+4} =\sqrt{29}[/tex] units.
YZ = [tex]\sqrt{(1-1)^2+(9-5)^2} =\sqrt{0+16} =\sqrt{16}[/tex] = 4 units.
XZ = [tex]\sqrt{(1-6)^2+(9-7)^2} =\sqrt{25+4} =\sqrt{29}[/tex] units.
Here,
XY = XZ, hence it is an isosceles triangle.
To learn more about Distance formula, here:-
https://brainly.com/question/8283882
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