Question

The coordinates of point R are (-3,2) and the coordinates of point T are (4,1). What is the length of RT?

Answer 1

In the following image we represent the position of the points R and T in the cartesian plane:

To find the distance between the points we draw a right triangle between them:

Where the resulting triangle has legs of measure 1 and 7, and "d" is the distance between the points.

If we call the legs

a=1

and b=7

Using the Pythagorean theorem, the formula to find "d" is as follows:

$d=\sqrt[]{a^2+b^2}$

Next, we substitute the values for the legs a and b:

$d=\sqrt[]{1^2+7^2}$

and we solve this operations:

$\begin{gathered} d=\sqrt[]{1+49} \\ d=\sqrt[]{50} \end{gathered}$

The distance is square root of 50.

If you need it, we can simplify the square root of the answer as follows:

$d=\sqrt[]{50}=\sqrt[]{25\times2}=5\sqrt[]{2}$

So the answer is:

$\sqrt[]{50}=5\sqrt[]{2}$