Midpoint Of A Line


Video Tutorial on Mid Point

Examples

Example 1
Find midpoints from 2 endpoints

What is the midpoint of A (2, 14) and B (4, 6)?

$$ A ( \color{Red}{2}, \color{Green}{14} ) \text{ and }B ( \color{Red}{4} , \color{Green}{6} ) \\ Midpoint = \Big( \frac{ \color{Red}{x_2 + x_1}}{2} , \frac{\color{Green}{y_2 + y_1}}{2} \Big) \\ \Big( \frac{\color{Red}{2 + 4} }{ 2} , \frac{\color{Green}{14 + 6} }{ 2} \Big) = \Big( \frac{ 6 }{ 2} , \frac{ 20 }{ 2} \Big) \\ Midpoint = (3, 10) $$

Example 2
Find end point from midpoint and other end point

If point X, the midpoint of segment AB, has coordinates(-4,9) and the coordinates of point A are (1,3), what are the coordinates of point B?

given endpoint and midpoint

Practice Problems

Problem 1

What is the midpoint of segment AB, given A(1,2) and B(7,4)?

Picture of Midpoint
Problem 2

What is the midpoint of A (4, 7 ) and B (-8 , 15)?

This is like example 1 above.

$$ A ( \color{Red}{4}, \color{Green}{ 7 } ) \text{ and }B ( \color{Red}{-8} , \color{Green}{ 15 } ) \\ Midpoint = \Big( \frac{ \color{Red}{x_2 + x_1}}{2} , \frac{\color{Green}{y_2 + y_1}}{2} \Big) \\ \Big( \frac{\color{Red}{4 + -8} }{ 2} , \frac{\color{Green}{7 + 15} }{ 2} \Big) = \Big( \frac{ -4}{ 2} , \frac{22}{ 2} \Big) \\ Midpoint = (-2,11) $$

Problem 3

If point X, the midpoint of segment AB , has coordinates(-1, 9 ) and the coordinates of point A are ( 3 , 7 ), what are the coordinates of point B?

Calculate how far you 'went' from the given endpoint to the midpoint (we went -4 in x and +4 in y)

midpoint

Go the same amount in the x and y directions

Problem 4

What is the midpoint of A (-2, 3 ) and B (-10 , 12)?

This is like example 2 above.

$$ A ( \color{Red}{-2}, \color{Green}{ 3 } ) \text{ and }B ( \color{Red}{-10} , \color{Green}{ 12 } ) \\ Midpoint = \Big( \frac{ \color{Red}{x_2 + x_1}}{2} , \frac{\color{Green}{y_2 + y_1}}{2} \Big) \\ \Big( \frac{\color{Red}{-2 + -10} }{ 2} , \frac{\color{Green}{3 + 12} }{ 2} \Big) = \Big( \frac{ -12}{ 2} , \frac{15}{ 2} \Big) \\ Midpoint = (-6,7.5) $$


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