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Equation of Parallel Line and Midpoint Calculation

This text explains how to find the equation of a line parallel to a given line and how to calculate the midpoint of line segments. It also includes examples and practice problems.

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Equation of Parallel Line and Midpoint Calculation

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  1. Warm up Write the equation of the line: Parallel (∥) to 8x – 2y = 6 and goes through (5, -2) in Standard form

  2. Midpoint Given 2 ordered pairs, it’s the AVG of the x’s and AVG of the y’s.

  3. Midpoint Formula

  4. Find the midpoint. (.5, 5.5) 1. (3, 7) and (-2, 4) 2. (5, -2) and (6, 14) (5.5, 6)

  5. Find the midpoint. 3. (3, -9) and (14, 16) 4. (12, 17) and (-7, 9) (8.5, 3.5) (2.5, 13)

  6. Find the midpoint. 5. (2, 3)

  7. Find the midpoint. 6. (1.5, 4)

  8. Given the midpt and one endpt, find the other endpt. 7. Midpt (3, -6) Endpt (7, -3) (-1, -9)

  9. Given the midpt and one endpt, find the other endpt. 8. Midpt (-1, 2) Endpt (3, 0) (-5, 4)

  10. Given the midpt and one endpt, find the other endpt. 9. Midpt (-4, 6) Endpt (2, 1) (-10, 11)

  11. Partition Line Segments(1 Dimension)

  12. Partition – 1 Dimension • A is at 1, and B is at 7. • Find the point, T, so that T partitions A to B in a 2:1 ratio.

  13. Partition – 1 Dimension • A is at -6 and B is at 4. • Find the point, T, so that T is A to B in a 2:3 ratio.

  14. Find a Point that Partitions a Segment in a Given Ratio a:b

  15. Find the coordinates of P along the directed line segment AB so that the ratio of AP to PB is 3 to 2. In order to divide the segment in the ratio of 3 to 2, think of dividing the segment into 3 + 2 or 5 congruent pieces.

  16. A(3, 4), B(6, 10); 3 to 2. 3 AB has a rise of 6. 6 AB has a run of 3.

  17. A(3, 4), B(6, 10); 3 to 2. To find the coordinates of point P… 3 6

  18. Example 1: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(1, 3), B(8, 4); 4 to 1.

  19. Example 2: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-2, 1), B(4, 5); 3 to 7.

  20. Example 3: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(8, 0), B(3, -2); 1 to 4.

  21. Example 4: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-2, -4), B(6, 1); 3 to 2.

  22. Partitioning Segments Worksheet Homework

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