On a coordinate plane, 3 triangles are shown. Triangle D E F has points (5, negative 2), (1, negative 2), (1, negative 4). Triangle D prime E prime F prime has points (2, 5), (2, 1), (4, 1). Triangle D double-prime E double-prime F double-prime has points (negative 3, 5), (negative 3, 1), (negative 1, 1). Which rule describes the composition of transformations that maps ΔDEF to ΔD''E''F''?

R0,90° ∘ T5,0(x, y)
T–5,0 ∘ R0,90°(x, y)
T5,0 ∘ R0,90°(x, y)
R0,90°(x, y) ∘ T–5,0

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

1. sometimes

2. never true

3. sometimes

step-by-step explanation:

these are pretty self explanatory if you know what supp right and com angles are