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(2,4)

(12, 8)

2.1 Determining the Midpoint of a Line Segment

(7,6)

Find the midpoint between the points (2, 4) and (12, 8)

2 12

4

8

7

6

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(6, –9)

(–2, 3)

(2, –3)

Find the midpoint between the points (–2, 3) and (6, –9)

–2 62

–9

3

–3

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Find the midpoint between the points (x1, y1) and (x2, y2)

(x2, y2)

(x1, y1)

1 2 1 2,2 2

x x y yM

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Determine the midpoint between the points (–9, 4) and (1, 14)

1 2 1 2,2 2

x x y yM

(x1, y1) (x2, y2)

9 1 4 14,

2 2M

8 18,

2 2M

M = (– 4, 9)

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If one end of a line segment AB is A(–5, 1) and the midpoint of the line segment is M(–1, 6), determine the coordinates of point B.

A(–5, 1)

M(–1, 6)

(3, 11)

4

4

5

5

B(3, 11)

MAC x1 x2

2, y1 y2

2

1, 6 5 x2

2,

1 y2

2

1 5 x2

26

1 y2

2

2 5 x2 12 1 y2

2 5 x2 12 1y2

3 x2 11 y2

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If one end of a line segment CD is C(3, -4) and the midpoint of the line segment is M(1, 2), determine the coordinates of point D.

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The coordinates of a rectangle are A(0, 8), B(9, 10), C(11, 2), D(2, 0). Determine if the midpoints of the diagonals are the same.

A(0, 8)

B(9, 10)

C(11, 2)

D(2, 0)

0 11 8 2,

2 2ACM

5.5,5ACM

2 9 0 10,

2 2DBM

5.5,5DBM

The midpoints of the diagonals are the same.