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Randy wants to draw isosceles right triangles on a coordinate plane that have two vertices at (-1,6) and (-1,-2). If the coordinates of the third vertex are both integers, how many different isosceles right triangles can she draw?

Respuesta :

xero099

Answer:

Two isosceles right triangles. [tex]p_{3} = (-9,-2)[/tex] and [tex]p_{3'} = (7,-2)[/tex]

Step-by-step explanation:

The length of one side is:

[tex]l_{1} = \sqrt{[-1 - (-1)]^{2}+[6 - (-2)]^{2}}[/tex]

[tex]l_{1} = 8[/tex]

An isosceles right has two sides of identical length, which are both legs and perpendicular to each other. There are two possibilities:

[tex]p_{3} = (-1 - 8, -2)[/tex]

[tex]p_{3} = (-9,-2)[/tex]

[tex]p_{3'} = (-1 + 8, -2)[/tex]

[tex]p_{3'} = (7,-2)[/tex]

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