--- id: 5900f3c71000cf542c50feda challengeType: 5 title: 'Problem 91: Right triangles with integer coordinates' forumTopicId: 302208 --- ## Description

The points P (x₁, y₁) and Q (x₂, y₂) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form ΔOPQ. a graph plotting points P (x_1, y_1) and Q(x_2, y_2) at integer coordinates that are joined to the origin O (0, 0)

a graph plotting points P (x_1, y_1) and Q(x_2, y_2) at integer coordinates that are joined to the origin O (0, 0)

There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between 0 and 2 inclusive; that is, 0 ≤ x₁, y₁, x₂, y₂ ≤ 2. a diagram showing the 14 triangles containing a right angle that can be formed when each coordinate is between 0 and 2

a diagram showing the 14 triangles containing a right angle that can be formed when each coordinate is between 0 and 2

Given that 0 ≤ x₁, y₁, x₂, y₂ ≤ 50, how many right triangles can be formed?

## Instructions

## Tests

```yml tests: - text: rightTrianglesIntCoords() should return a number. testString: assert(typeof rightTrianglesIntCoords() === 'number'); - text: rightTrianglesIntCoords() should return 14234. testString: assert.strictEqual(rightTrianglesIntCoords(), 14234); ```

## Challenge Seed

```js function rightTrianglesIntCoords() { return true; } rightTrianglesIntCoords(); ```

## Solution

```js // solution required ```