Question

Which statement proves that △XYZ is an isosceles right triangle?

XZ ⊥ XY
XZ = XY = 5
The slope of XZ is , the slope of XY is , and XZ = XY = 5.
The slope of XZ is , the slope of XY is , and the slope of ZY = 7.

Answer 1

The second statement does lol

Answer 2

XZ = XY = 5 units are equal .

ΔXYZ is a Right isosceles triangle .

Explanation:

As to an triangle is isosceles triangles the two sides of the triangle must be equal .

Formula

`Distance\ formula = \sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}`

As the vertices of the ΔXYZ be X (1,3) , Y (4,-1) and Z(5,6) .

`XY = \sqrt{(4-1)^(2)+(-1-3)^(2)}`

`XY = \sqrt{(3)^(2)+(-4)^(2)}`

`XY = √(9+16)`

`XY = √(25)`

`√(25)= 5`

`XY = 5\ units`

`YZ = \sqrt{(5-4)^(2)+(6-(-1))^(2)}`

`YZ = \sqrt{(1)^(2)+(7)^(2)}`

`YZ = √(1+49)`

`YZ = √(50)\ units`

`ZX = \sqrt{(1-5)^(2)+(3-6)^(2)}`

`ZX = \sqrt{(-4)^(2)+(-3)^(2)}`

`ZX = √(16+9)`

`ZX = √(25)`

`√(25)= 5`

ZX = 5 units

Thus XZ = XY = 5 units are equal .

Therefore ΔXYZ is a Right isosceles triangle .