Triangle abc has vertices at ac-3, 4), b(4, -2), c(8.3). the triangle is translated 4 units down and 3 units left. which rule
represents the translation. after the translation, what are the coordinates of vertex c?
(x, y)= (x + 3. y + 4); (11,7)
b)
(x, y) - x - 4, y + 3): -6,7)
(xy) - (x - 3. y - 4); (5.-1)
(x, y) -
-2,- 1)

Part a) The rule of the translation is (x,y) > (x-3,y-4)

Part b) The coordinates of vertex C after translation is (5,-1)

Step-by-step explanation:

Part a) Which rule  represents the translation

we know that

The triangle is translated 4 units down > That means that the new y-coordinate is equal to the original y-coordinate minus 4

The triangle is translated 3 units left > That means that the new x-coordinate is equal to the original x-coordinate minus 3

so

The rule of the translation is

(x,y) > (x-3,y-4)

Part b) Find the coordinates of vertex  after translation

Applying the rule of the translation to vertex C

C(8.3) > C'(8-3,3-4)

C(8.3) > C'(5,-1)

, 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