Midpoint of Line Joining Two Points

If A, B are the points (x₁, y₁),(x₂, y₂) and (x_c, y_c) is the midpoint of line AB as shown in the diagram below

Then AC = CB, also AD = DE or x_c – x₁ = x₂ – x_c

i.e x_c = ½ (x₁ + x₂)

and y_c = ½ (y₁+y₂)

So the coordinates of the midpoint of (x₁,y₁) and (x₂,y₂) are

\( \left [ \frac{1}{2} \scriptsize (x_1 \; + \; x_2), \normalsize \frac{1}{2} \scriptsize (y_1 \; + \; y_2) \right ] \)

Example

Solution

a. x₁ = 2, y₁ = 3

x₂ = 4, y₂ = 7

∴ { ½ (2 + 4), ½ (3 + 7)}

{ ½ (6), ½ (10)}

{3, 5}

b. x₁ = -1, y₁ = 3

x₂ = 5,  y₂ = -4

∴ { ½ ((-1) + 5),  ½ (3 + (-4)}

  { ½ (4),  ½ (-1)}

  {2, – ½ }