Question

calculate midpoint of (8,4) and (12,2)

Answer 1

The formula of a midpoint:

$M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)$

We have:

$A(8,\ 4)\to x_A=8,\ y_A=4\\B(12,\ 2)\to x_B=12,\ y_B=2$

Substitute:

$\dfrac{8+12}{2}=\dfrac{20}{2}=10\\\\\dfrac{4+2}{2}=\dfrac{6}{2}=3$

Answer: (10, 3).

Answer 2

Let's first recall what is known as the Midpoint formula we have, so by the Midpoint formula, we know that, the midpoint of any line segment joining the points ${\bf{A(x_{1},y_{1})}}$ and ${\bf{B(x_{2},y_{2})}}$ is given by

• ${\boxed{\bf{M(x,y)=\bigg(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2}\bigg)}}}$

Now, if we assume our points to be A(8,4) and B(12,2) and the midpoint being M, then we will be having :

${:\implies \quad \sf M=\bigg(\dfrac{8+12}{2},\dfrac{4+2}{2}\bigg)}$

${:\implies \quad \sf M=\bigg(\dfrac{20}{2},\dfrac{6}{2}\bigg)}$

${:\implies \quad \boxed{\bf{M=(10,3)}}}$

Hence, the required Midpoint is (10,3)