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Point X is located at (3,2). Point Y is located at (3,-8). What is the distance from point X to point Y ?

Point X X is located at (3,2) (3,2) . Point Y Y is located at (3,−8) (3,-8) .\newlineWhat is the distance from point X X to point Y Y ?

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Full solution

Q. Point X X is located at (3,2) (3,2) . Point Y Y is located at (3,−8) (3,-8) .\newlineWhat is the distance from point X X to point Y Y ?
  1. Identify Points: Identify the coordinates of point XX and point YY. Point XX is at (3,2)(3,2) and point YY is at (3,−8)(3,-8).
  2. Distance Formula: Use the distance formula to calculate the distance between two points in a plane. The distance formula is:\newlineDistance = [(x2−x1)2+(y2−y1)2]\sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\newlineWhere (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of the two points.
  3. Substitute Coordinates: Substitute the coordinates of point XX and point YY into the distance formula.\newlineDistance = [(3−3)2+(−8−2)2]\sqrt{[(3 - 3)^2 + (-8 - 2)^2]}
  4. Simplify Equation: Simplify the equation by performing the operations inside the square root. \newlineDistance = (0)2+(−10)2\sqrt{\left(0\right)^2 + \left(-10\right)^2}
  5. Calculate Squares: Calculate the squares of the differences.\newlineDistance = 0+100\sqrt{0 + 100}
  6. Simplify Square Root: Simplify the square root.\newlineDistance = 100\sqrt{100}
  7. Calculate Final Distance: Calculate the final value of the distance.\newlineDistance = 1010

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