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Develop and apply the formula for midpoint.

Objectives. Develop and apply the formula for midpoint. Use the Distance Formula to find the distance between two points. Example 1: Finding the Coordinates of a Midpoint. Find the coordinates of the midpoint of PQ with endpoints P (–8, 3) and Q (–2, 7). = (–5, 5).

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Develop and apply the formula for midpoint.

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  1. Objectives Develop and apply the formula for midpoint. Use the Distance Formula to find the distance between two points.

  2. Example 1: Finding the Coordinates of a Midpoint Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7). = (–5, 5)

  3. Example 2: Finding the Coordinates of an Endpoint M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y. Step 1 Let the coordinates of Y equal (x, y). X M Y (2,7) (6,1) (x,y)

  4. – 2 – 7 –2 –7 Example 2 Continued Step 2 Set the coordinates equal. Multiply both sides by 2. 12 = 2 + x Simplify. 2 = 7 + y Subtract. –5 = y 10 = x Simplify. The coordinates of Y are (10, –5).

  5. Find FG and JK. Then determine whether FG  JK. Example 3: Using the Distance Formula Step 1 Find the coordinates of each point. F(1, 2), G(5, 5), J(–4, 0), K(–1, –3)

  6. Example 3 Continued Step 2 Use the Distance Formula.

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