It's easier to find the lengths of horizontal and vertical segments.
It's easier to find the length of a segment if one endpoint is at the origin.
(0,0), (0,5d) and (5d,0).
Practice makes perfect
When we place a triangle in a coordinate plane for the purpose of doing a proof, we should consider the following:
It's easier to find the lengths of horizontal and vertical segments.
It's easier to find the lengths of a segment if one endpoint is at the origin.
Let's draw the given triangle and check if the triangle has been placed in a way that supports the two statements. Note that we will assume that d is a positive value.
As we can see, the triangle has one vertical side and one horizontal side which means this is a right triangle. To figure out a better placement, we should first determine the length of the triangles legs.
We are working with a right isosceles triangle with legs of length 5d. Therefore, a better placement would be one where the right angle vertex is at the origin, one leg runs along the vertical axis and the other along the horizontal axis.
The coordinates should be (0,0), (0,5d) and (5d,0).
