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The coordinates of the point 
O are 
(3,-5) and the coordinates of point 
P are 
(8,-5). What is the distance, in units, between the point 
O and point 
P ?
Answer: units

The coordinates of the point O O are (3,5) (3,-5) and the coordinates of point P P are (8,5) (8,-5) . What is the distance, in units, between the point O O and point P P ?\newlineAnswer: \square units

Full solution

Q. The coordinates of the point O O are (3,5) (3,-5) and the coordinates of point P P are (8,5) (8,-5) . What is the distance, in units, between the point O O and point P P ?\newlineAnswer: \square units
  1. Identify formula: Identify the formula to calculate the distance between two points in a coordinate plane.\newlineThe distance between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) in a coordinate plane is given by the formula:\newlineDistance = ((x2x1)2+(y2y1)2)\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}
  2. Plug in coordinates: Plug in the coordinates of points O and P into the distance formula.\newlineFor point O, we have (x1,y1)=(3,5)(x_1, y_1) = (3, -5) and for point P, we have (x2,y2)=(8,5)(x_2, y_2) = (8, -5).\newlineDistance = ((83)2+(5(5))2)\sqrt{((8 - 3)^2 + (-5 - (-5))^2)}
  3. Simplify expression: Simplify the expression inside the square root.\newlineCalculate the difference between the xx-coordinates: 83=58 - 3 = 5\newlineCalculate the difference between the yy-coordinates: 5(5)=0-5 - (-5) = 0\newlineDistance = (52+02)\sqrt{(5^2 + 0^2)}
  4. Calculate squares and add: Calculate the squares of the differences and add them.\newline52=255^2 = 25\newline02=00^2 = 0\newlineDistance = 25+0\sqrt{25 + 0}
  5. Simplify square root: Simplify the square root. 25=5\sqrt{25} = 5 Distance = 55

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