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Objective: 1) To find the distance between two points in the coordinate plane.

Ch 1.8 Standard 17.0: Students prove theorems by using coordinate geometry, including the midpoint of a line segment and the distance formula. Objective: 1) To find the distance between two points in the coordinate plane.

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Objective: 1) To find the distance between two points in the coordinate plane.

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  1. Ch 1.8Standard 17.0: Students prove theorems by using coordinate geometry, including the midpoint of a line segment and the distance formula. Objective: 1) To find the distance between two points in the coordinate plane. 2) To find the coordinates of the midpoint of a segment in the coordinate plane.

  2. Definition A coordinate planeis a plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis) . The location, or coordinates, of a point are given by an ordered pair (x, y). F = (1, 2) G = (5, 5) J = (-4, 0) K = (-1, -3)

  3. Midpoint Formula You can find themidpointof a segment by using the coordinates of its endpoints. Calculate the average of the x-coordinates and the average of the y-coordinates of the endpoints.

  4. Example (Midpoint) Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7). = (–5, 5)

  5. Distance Formula The Distance Formula is used to calculate the distance between two points in a coordinate plane.

  6. Example (Distance) Find the distance of FG. Step 1 Find the coordinates of each point. F = (1, 2) G = (5, 5) Step 2 Use the Distance Formula.

  7. Another Example (Distance) Find the distance of JK. Step 1 Find the coordinates of each point. J = (-4, 0) K = (-1, -3) Step 2 Use the Distance Formula.

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