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If W(-10, 4), X(-3, -1), and Y(-5, 11) classify triangle WXY by its sides.



Hint! Use Distance Formula! (Its on the word wall if you don't remember it)

Respuesta :

frika

Answer:

The triangle WXY is an isoscels triangle with the base XY

Step-by-step explanation:

In the triangle WXY, W(-10, 4), X(-3, -1), and Y(-5, 11). Find the lengths of all sides of the triangle WXY as distances between points:

[tex]WX=\sqrt{(-10-(-3))^2+(4-(-1))^2}=\sqrt{(-10+3)^2+(4+1)^2}=\sqrt{49+25}=\sqrt{74}\ units\\ \\XY=\sqrt{(-3-(-5))^2+(-1-11)^2}=\sqrt{(-3+5)^2+(-12)^2}=\sqrt{4+144}=\sqrt{148}\ units\\ \\WY=\sqrt{(-10-(-5))^2+(4-11)^2}=\sqrt{(-10+5)^2+(-7)^2}=\sqrt{25+49}=\sqrt{74}\ units[/tex]

There are two congruent sides WX and WY, so the triangle WXY is an isoscels triangle with the base XY

akposevictor

There are two congruent sides (WX and WY) in triangle WXY, triangle WXY can be classified based by its sides as: an isosceles triangle.

Recall:

  • Two of the sides of an Isosceles triangle are equal (congruent).
  • Distance formula is: [tex]\mathbf{d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}}[/tex]

Given the vertices of a triangle WXY have the following coordinates:

W(-10, 4)

X(-3, -1)

Y(-5, 11)

We need to know the length of its sides, WX, XY, and WY in other to classify the triangle by its side.

Thus, applying the distance formula:

  • Find WX:

[tex]WX = \sqrt{(-1 - 4)^2 + (-3 -(-10))^2}\\\\WX = \sqrt{(-5)^2 + (7)^2}\\\\\mathbf{WX = \sqrt{74} }[/tex]

  • Find XY:

[tex]XY = \sqrt{(11 - (-1))^2 + (-5 -(-3))^2}\\\\XY = \sqrt{(12)^2 + (-2)^2}\\\\\mathbf{XY = \sqrt{148} }[/tex]

  • Find WY:

[tex]WY = \sqrt{(11 - 4)^2 + (-5 -(-10))^2}\\\\WY = \sqrt{(7)^2 + (5)^2}\\\\\mathbf{WY = \sqrt{74} }[/tex]

There are two congruent sides (WX and WY) in triangle WXY, triangle WXY can be classified based by its sides as: an isosceles triangle.

Learn more here:

https://brainly.com/question/15339657

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