Question

find the distance between (14,-6) and (12,8)

Answer 1

For explanation purposes I'll call Point A (14,-6) and Point B (12,8) the given points.

To calculate the distance between both points you have to calculate the distance between each coordinate over the x and y axis.

Then apply the Phytagoras theorem to calculate its length.

I'll sketch the points:

x-axis

$base=d_{AB}=x_A-x_B=14-12=2$

y-axis

$heigth=d_{AB}=y_B-y_A=8-(-6)=8+6=14$

Now according to the Phythagoras theorem, the sum of the squared base and the squared heigth of a triangle is equal to the squared hypotenuse:

$a^2+b^2=c^2$

For this triangle:

$\begin{gathered} 2^2+14^2=c^2 \\ c^2=200 \\ c=\sqrt[]{200}=10\sqrt[]{2}=14.14 \end{gathered}$

The distance between both points is 14.14 units.