Question

There are twelve points, each with integer coordinates, that are 10 units from the origin. List the points. (Hint: Recall the 6, 8, 10 right triangle.)

Short answer

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

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

Step-by-step solution

Step-1 – Given

Given that: There are twelve points, each with integer coordinate, that are 10 units from the origin. Recall the 6,8,10 right triangle.

Step-2 – To determine

We have to find the points.

Step-3 – Calculation

We first take the coordinates 10 units from the origin on the x and y-axis.

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

After that, we make the coordinate 6,8,10 points

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

It means, the points are $\left(10,0\right),\left(0,10\right),\left(-10,0\right),\left(0,-10\right)$

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