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Point W is located at (-5,-3). Select all of the following that are 5 units from point W. Choose all answers that apply: A (-8,-5) B (-5,0) c (-5,2)

Point W W is located at (−5,−3) (-5,-3) .\newlineSelect all of the following that are 55 units from point W W .\newlineChoose all answers that apply:\newline(A) (−8,−5) (-8,-5) \newline(B) (−5,0) (-5,0) \newline(C) (−5,2) (-5,2)

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Full solution

Q. Point W W is located at (−5,−3) (-5,-3) .\newlineSelect all of the following that are 55 units from point W W .\newlineChoose all answers that apply:\newline(A) (−8,−5) (-8,-5) \newline(B) (−5,0) (-5,0) \newline(C) (−5,2) (-5,2)
  1. Understand the problem: Understand the problem.\newlineWe need to find points that are 55 units away from point WW, which is at (−5,−3)(-5,-3). This means we are looking for points that have a distance of 55 units from WW in any direction.
  2. Use distance formula for point A: Use the distance formula to check point A (−8,−5)(-8,-5).\newlineThe distance formula is d=((x2−x1)2+(y2−y1)2)d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}, where (x1,y1)(x_1, y_1) is point W and (x2,y2)(x_2, y_2) is point A.\newlineFor point A (−8,−5)(-8,-5), we calculate:\newlined=((−8−(−5))2+(−5−(−3))2)d = \sqrt{((-8 - (-5))^2 + (-5 - (-3))^2)}\newlined=((−8+5)2+(−5+3)2)d = \sqrt{((-8 + 5)^2 + (-5 + 3)^2)}\newlined=(−3)2+(−2)2d = \sqrt{(-3)^2 + (-2)^2}\newlined=9+4d = \sqrt{9 + 4}\newlined=13d = \sqrt{13}\newlineSince d=((x2−x1)2+(y2−y1)2)d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}00 is not equal to d=((x2−x1)2+(y2−y1)2)d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}11, point A is not d=((x2−x1)2+(y2−y1)2)d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}11 units away from point W.
  3. Use distance formula for point B: Use the distance formula to check point B (−5,0)(-5,0).\newlineFor point B (−5,0)(-5,0), we calculate:\newlined=((−5−(−5))2+(0−(−3))2)d = \sqrt{((-5 - (-5))^2 + (0 - (-3))^2)}\newlined=(0)2+(3)2d = \sqrt{(0)^2 + (3)^2}\newlined=0+9d = \sqrt{0 + 9}\newlined=9d = \sqrt{9}\newlined=3d = 3\newlineSince 33 is not equal to 55, point B is not 55 units away from point W.
  4. Use distance formula for point C: Use the distance formula to check point C (−5,2)(-5,2).\newlineFor point C (−5,2)(-5,2), we calculate:\newlined=((−5−(−5))2+(2−(−3))2)d = \sqrt{((-5 - (-5))^2 + (2 - (-3))^2)}\newlined=(0)2+(5)2d = \sqrt{(0)^2 + (5)^2}\newlined=0+25d = \sqrt{0 + 25}\newlined=25d = \sqrt{25}\newlined=5d = 5\newlineSince 55 is equal to 55, point C is 55 units away from point W.

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