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

its C

Explanation:

yw :)

Answer 2

The slope of XZ is 3/4 , the slope of XY is -4/3 , and XZ = XY = 5 ⇒ 3rd answer

Explanation:

* Lets look to the attached figure to solve the problem

- To prove that the Δ XYZ is an isosceles right triangle, you must

find two sides the product of their slopes is -1 and they are equal

in lengths

- From the figure the vertices of the triangle are;

X = (1 , 3) , Y = (4 , -1) , Z = (5 , 6)

- The slope of the line whose endpoints are (x1 , y1) and (x2 , y2)

is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

∵ The slope of
`XY=(-1-3)/(4-1)=(-4)/(3)`

∵ The slope of
`XZ=(6-3)/(5-1)=(3)/(4)`

∴ The slope of XY = -4/3 , the slope of XZ = 3/4

∵ -4/3 × 3/4 = -1

∴ XY ⊥ XZ

∴ ∠ X is a right angle

∴ Δ XYZ is a right triangle

- The distance between the two points (x1 , y1) and (x2 , y2) is

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

∵
`XY=\sqrt{(4-1)^(2)+(-1-3)^(2)}=√(9+16)=√(25)=5`

∵
`XZ=\sqrt{(5-1)^(2)+(6-3)^(2)}=√(16+9)=√(25)=5`

∴ XY = XZ = 5

∴ Δ XYZ is an isosceles right triangle

* The statement which prove that is:

The slope of XZ is 3/4 , the slope of XY is -4/3 , and XZ = XY = 5