CAN SOMEONE PLS ANSWER-If W(- 10, 4), X(- 3, - 1) , and Y(- 5, 11) classify AEXY by its sides . Show all work to justify your answer

CAN SOMEONE PLS ANSWERIf W 10 4 X 3 1 And Y 5 11 Classify AEXY By Its Sides Show All Work To Justify Your Answer class=

Sagot :

Answer:

  • WX = [tex]\sqrt{74} \approx 8.6023253\\\\[/tex]
  • XY = [tex]2\sqrt{37} \approx 12.1655251\\\\[/tex]
  • WY = [tex]\sqrt{74} \approx 8.6023253\\\\[/tex]
  • Classify:  Isosceles

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Explanation:

Apply the distance formula to find the length of segment WX

W = (x1,y1) = (-10,4)

X = (x2,y2) = (-3, -1)

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-10-(-3))^2 + (4-(-1))^2}\\\\d = \sqrt{(-10+3)^2 + (4+1)^2}\\\\d = \sqrt{(-7)^2 + (5)^2}\\\\d = \sqrt{49 + 25}\\\\d = \sqrt{74}\\\\d \approx 8.6023253\\\\[/tex]

Segment WX is exactly [tex]\sqrt{74}[/tex] units long which approximates to roughly 8.6023253

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Now let's find the length of segment XY

X = (x1,y1) = (-3, -1)

Y = (x2,y2) = (-5, 11)

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-(-5))^2 + (-1-11)^2}\\\\d = \sqrt{(-3+5)^2 + (-1-11)^2}\\\\d = \sqrt{(2)^2 + (-12)^2}\\\\d = \sqrt{4 + 144}\\\\d = \sqrt{148}\\\\d = \sqrt{4*37}\\\\d = \sqrt{4}*\sqrt{37}\\\\d = 2\sqrt{37}\\\\d \approx 12.1655251\\\\[/tex]

Segment XY is exactly [tex]2\sqrt{37}[/tex] units long which approximates to 12.1655251

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Lastly, let's find the length of segment WY

W = (x1,y1) = (-10,4)

Y = (x2,y2) = (-5, 11)

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-10-(-5))^2 + (4-11)^2}\\\\d = \sqrt{(-10+5)^2 + (4-11)^2}\\\\d = \sqrt{(-5)^2 + (-7)^2}\\\\d = \sqrt{25 + 49}\\\\d = \sqrt{74}\\\\d \approx 8.6023253\\\\[/tex]

We see that segment WY is the same length as WX.

Because we have exactly two sides of the same length, this means triangle WXY is isosceles.