What is the perimeter of a triangle with corners at $(3 ,4 )$ , $(6 ,7 )$ , and $(4 ,5 )$ ?

Question

1419 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-02T13:44:31

$color(blue)("No triangle exists")$

Labelling the points:

$A=(3,4), B=(6,7), C=(4,5)$

Vectors:

$vec(AB)=((3),(3))$

$vec(AC)=((1),(1))$

$vec(AC)=mu((3),(3))color(white)(888888)$ , for $mu=1/3$

$:.$

$vec(AC)=1/3vec(AB)$

This means the points are collinear ( all lying on a straight line ), so these points do not form a triangle.

What is the perimeter of a triangle with corners at (3 ,4 )(3 ,4 ), (6 ,7 )(6 ,7 ), and (4 ,5 )(4 ,5 )?