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Warm Up Simplify. 1. 7 – (–3) 2. –1 – (–13) 3. | –7 – 1| Solve each equation.

Warm Up Simplify. 1. 7 – (–3) 2. –1 – (–13) 3. | –7 – 1| Solve each equation. 4. 2 x + 3 = 9 x – 11 5. 3 x = 4 x – 5 6. How many numbers are there between and ?. 10. 12. 8. 2. 5. Infinitely many. Distance and Midpoints. Section 1-3. Midpoint of a segment.

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Warm Up Simplify. 1. 7 – (–3) 2. –1 – (–13) 3. | –7 – 1| Solve each equation.

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  1. Warm Up Simplify. 1.7 – (–3) 2. –1 – (–13) 3. |–7 – 1| Solve each equation. 4. 2x + 3 = 9x – 11 5. 3x = 4x – 5 6. How many numbers are there between and ? 10 12 8 2 5 Infinitely many

  2. Distance and Midpoints Section 1-3

  3. Midpoint of a segment • midpoint of a segment: • Segment Bisector: • If M is the midpoint of AB, then… • So if AB = 6, then… A M B

  4. Example: - D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Solve for x. E D F 4x + 6 7x – 9

  5. Finding the midpoint of a segment • You can find the midpoint of a segment by using the coordinates of its endpoints.

  6. The Coordinate Plane Origin (0, 0) X-axis (horizontal) Y-axis (vertical)

  7. Finding the midpoint of coordinates • On the coordinate plane it is more involved. • We will need to calculate the average of the x-coordinates and the average of the y-coordinates of the two endpoints.

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

  9. Example:Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3). Midpoint of EF = (1.5, 0)

  10. Example: M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y. X has the coordinate (10, -5)

  11. Example: S is the midpoint of RT. R has coordinates (–6, –1), and S has coordinates (–1, 1). Find the coordinates of T. The coordinates of T are (4, 3).

  12. Distance Formula • To calculate distance between 2 points on the coordinate plane. • Comes from the Pythagorean Theorem.

  13. Use the Pythagorean Theorem. Count the units for sides a and b. c2 =a2 + b2

  14. Example - Use the Pythagorean Theorem to find the distance, to the nearest tenth, from D(3, 4) to E(–2, –5). c =10.3

  15. The Distance Formula • Use the Pythagorean Theorem to derive the Distance Formula. c2 =a2 + b2 c =10.3

  16. Example: Use the Distance Formula to find the length of line segment FG. ** F(1, 2), G(5, 5) FG = 5

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