Question

Together with the pair of points ( ,0) and (0, ), there are six points that could be the third vertex of an isosceles right triangle. Find the coordinates of each point.

Answer 1

To find the coordinates of the points that could be the third vertex of an isosceles right triangle along with the given pair of points, we need to use the properties of isosceles right triangles. An isosceles right triangle has two sides of equal length and one right angle. The possible coordinates for the third vertex would be (x1,y1), (y1,x1), (-x1,y1), (-y1,x1), (x1,-y1), and (y1,-x1).

Step-by-step explanation:

To find the coordinates of the points that could be the third vertex of an isosceles right triangle along with the given pair of points, we need to use the properties of isosceles right triangles.

An isosceles right triangle has two sides of equal length and one right angle.

Let's consider the given points (x1,0) and (0,y1). The possible coordinates for the third vertex would be (x1,y1), (y1,x1), (-x1,y1), (-y1,x1), (x1,-y1), and (y1,-x1). Based on the properties of isosceles right triangles, all of these points would form isosceles right triangles with the given pair of points.