Chapter 13.1, Problem 33WE

To determine

To find the points

Answer to Problem 33WE

The points are $\left(10,0\right),\left(0,10\right),\left(-10,0\right),\left(0,-10\right)$

  $\left(6,8\right),\left(6,10\right),\left(8,10\right),\left(8,6\right),\left(10,6\right),\left(10,8\right),\left(-6,8\right),\left(-6,10\right),\left(-8,10\right),\left(-8,6\right),\left(-10,6\right),\left(-10,8\right)$

Explanation of Solution

Given information:

There are twelve points, each with integer coordinate, that are 10 units from the origin

Recall the 6,8,10 right triangle

Calculation:

The points can be obtained as

Since the points 6,8,10 is given and the 10 units from the origin is also given

So, first make the coordinate 10 units from the origin

  $\left(10,0\right),\left(0,10\right),\left(-10,0\right),\left(0,-10\right)$

Again, make the coordinate 6,8,10 points

  $\begin{array}{l}\left(6,8\right),\left(6,10\right),\left(8,10\right),\left(8,6\right),\left(10,6\right),\left(10,8\right)\\ \left(-6,8\right),\left(-6,10\right),\left(-8,10\right),\left(-8,6\right),\left(-10,6\right),\left(-10,8\right)\end{array}$

Hence,

The points are $\left(10,0\right),\left(0,10\right),\left(-10,0\right),\left(0,-10\right)$

  $\left(6,8\right),\left(6,10\right),\left(8,10\right),\left(8,6\right),\left(10,6\right),\left(10,8\right),\left(-6,8\right),\left(-6,10\right),\left(-8,10\right),\left(-8,6\right),\left(-10,6\right),\left(-10,8\right)$