1. ## Triangle

Given points (0, –14), (18, 4). Find a third point so that the three points form the vertices of an isosceles triangle

2. Originally Posted by ailmasum
Given points (0, –14), (18, 4). Find a third point so that the three points form the vertices of an isosceles triangle
Easiest way is to reflect across y-axis.

3. Hello, ailmasum!

Who assigned this problem?
It's truly silly . . .

$\text{Given points }A(0, -14),\;B(18, 4).$

$\text{Find a third point }C\text{ so that }\Delta ABC\text{ is an isosceles triangle.}$
Code:
        |
|      ♥                B
|       ♥               o
|        ♥           *
|         ♥       *
- - + - - - - -♥- -*- - - -
|           *
|        *   ♥
|     *       ♥
|  *           ♥
o               ♥
|

$\,C$ can be (almost) any point on the perpendicular bisector of $AB.$

Code:
              * * *
*           *   B
*               o
*              *  *
*
*         A *       *
*         o         *
*      (0,-14)      *

*                 *
*               *
*           *
* * *

Consider the circle with center $\,A$ and radius $AB.$

$\,C$ can be (almost) any point on the circle.

Code:
              * * *
*           *
*               *
*                 *

*         B         *
*         o(18,4)   *
*       *           *
*
*  *              *
o               *
A   *           *
* * *

Consider the circle with center $\,B$ and radius $AB.$

$\,C$ can be (almost) any point on the circle.

4. Originally Posted by Soroban

It's truly silly . . .

I think it's a reasonable enough question. Suppose you were asked to solve it in under 10 seconds, or as part of some rapid-fire competition..