Question

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

Answer 1

• WX =
  `√(74) \approx 8.6023253\\\\`
• XY =
  `2√(37) \approx 12.1655251\\\\`
• WY =
  `√(74) \approx 8.6023253\\\\`
• Classify: Isosceles

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Step-by-step explanation:

Apply the distance formula to find the length of segment WX

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

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

`d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-10-(-3))^2 + (4-(-1))^2)\\\\d = √((-10+3)^2 + (4+1)^2)\\\\d = √((-7)^2 + (5)^2)\\\\d = √(49 + 25)\\\\d = √(74)\\\\d \approx 8.6023253\\\\`

Segment WX is exactly
`√(74)` 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)

`d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-3-(-5))^2 + (-1-11)^2)\\\\d = √((-3+5)^2 + (-1-11)^2)\\\\d = √((2)^2 + (-12)^2)\\\\d = √(4 + 144)\\\\d = √(148)\\\\d = √(4*37)\\\\d = √(4)*√(37)\\\\d = 2√(37)\\\\d \approx 12.1655251\\\\`

Segment XY is exactly
`2√(37)` 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)

`d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-10-(-5))^2 + (4-11)^2)\\\\d = √((-10+5)^2 + (4-11)^2)\\\\d = √((-5)^2 + (-7)^2)\\\\d = √(25 + 49)\\\\d = √(74)\\\\d \approx 8.6023253\\\\`

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.