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.
