On a coordinate plane, triangle X Y Z is shown. Point X is at (1, 3), point Y is at (4, negative 1), and point Z is at (5, 6).
Which statement proves that △XYZ is an isosceles right triangle?

XZ ⊥ XY
XZ = XY = 5
The slope of XZ is Three-fourths, the slope of XY is Negative four-thirds, and XZ = XY = 5.
The slope of XZ is Three-fourths, the slope of XY is Negative four-thirds, and the slope of ZY = 7.

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ghgjjvjvjjg ghgjjvjvjjg · Answer 1 · 2019-12-20T15:42:59+01:00

Answer:

C

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MrRoyal MrRoyal · Answer 2 · 2022-03-02T12:49:12+01:00

The statement that proves that triangle XYZ is an isosceles triangle is XZ = XY =5

isosceles triangles are triangles that have two equal sides

The coordinates are given as:

X = (1, 3)

Y = (4, -1)

Z = (5, 6)

Calculate the distances between the points using:

[tex]d =\sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]XY =\sqrt{(1 -4)^2 + (3 --1)^2}[/tex]

[tex]XY =5[/tex]

[tex]XZ =\sqrt{(1- 5)^2 + (3 -6)^2}[/tex]

[tex]XZ =5[/tex]

From the above computation, we have:

[tex]XY = XZ =5[/tex]

Hence, the statement that proves that triangle XYZ is an isosceles triangle is XZ = XY =5

Read more about isosceles triangles at:

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