Triangle DFE with coordinates D(0,0), F(3,0), and, E(3,1) is similar to triangle EHG. If vertex G has coordinates (9,3), what are the coordinates of vertex H?

Question

Triangle DFEDFE with coordinates D(0,0)D(0,0), F(3,0)F(3,0), and, E(3,1)E(3,1) is similar to triangle EHGEHG. If vertex GG has coordinates (9,3)(9,3), what are the coordinates of vertex HH?

Answer 1

An infinite number of possible vertices for similar triangls, but the EFE, EHG narrows it down

origin, D(0,0), F(3,0), E(3,1)

are three vertices of a right triangle with side lengths 3, 1 and sqr10

similar triangle is EHG, G corresponds to E

G(9,3) is 3 times (3,1) so multiply the other new vertex by 3 to get 3(3,0) = (9,0)

That's probably the answer you want.

Endless other similar right triangles are equally possible

such as (9,3), (10,4), (12,3)

or (9,3),(9,2), (6,2)

although those vertices describe congruent right triangles with both sides and angles equal to the original triangle. so they're not just similar but also congruent.

It might help to plot the ponts, draw the triangles and compare them.

As long as they have proportionate sides and the same angles, they're similar triangles

Eliminate any that don't follow the EHG DFE letter pattern