�RST with vertices R (-2, -2) , S (-3, 1) , and T (1, 1) is translated by

Question

�RST with vertices R (-2, -2) , S (-3, 1) , and T (1, 1) is translated by

(x, y) →
(x - 1, y + 3) . Then the image, �RST , is translated by

(x, y) →
(x + 4, y - 1) , resulting in �R "S"T ".
a. Find the coordinates for the vertices of �R "S"T ".

Answer 1

so we are doing:

(x,y) --->(x-1, y+3) ----> (x+4, y-1)

so for R(-2,-2)

(-2,-2) --->(-3, 1) ----> (1, 0)

do the same for the other points

(I am not sure why you have quotations around S and T in the final result. Are you saying that only S and T are transformed?
If so, then just apply the above to S and T, leaving R alone. If this had been my question , I would expect you to translate all 3 points, even have you graph the original, the intermediate and the final to show that congruency is maintained)

Answer 2

To find the coordinates for the vertices of RS'T', we first need to apply the translation (x, y) → (x - 1, y + 3) to the original triangle RST:

For point R (-2, -2):
x coordinate of R' = (-2) - 1 = -3
y coordinate of R' = (-2) + 3 = 1

For point S (-3, 1):
x coordinate of S' = (-3) - 1 = -4
y coordinate of S' = (1) + 3 = 4

For point T (1, 1):
x coordinate of T' = (1) - 1 = 0
y coordinate of T' = (1) + 3 = 4

So, the vertices of RS'T' are R'(-3, 1), S'(-4, 4), and T'(0, 4).

Answer 3

To find the coordinates for the vertices of �R "S"T ", we need to perform the translation step by step.

1. First, let's perform the translation given in the question: (x, y) → (x - 1, y + 3)

For vertex R(-2, -2):
The new coordinates for R will be:
x = -2 - 1 = -3
y = -2 + 3 = 1

So, the new coordinates for R are (-3, 1).

For vertex S(-3, 1):
The new coordinates for S will be:
x = -3 - 1 = -4
y = 1 + 3 = 4

So, the new coordinates for S are (-4, 4).

For vertex T(1, 1):
The new coordinates for T will be:
x = 1 - 1 = 0
y = 1 + 3 = 4

So, the new coordinates for T are (0, 4).

2. Next, let's perform the second translation: (x, y) → (x + 4, y - 1)

For vertex R(-3, 4):
The new coordinates for R will be:
x = -3 + 4 = 1
y = 4 - 1 = 3

So, the final coordinates for R in �R "S"T " are (1, 3).

For vertex S(-4, 4):
The new coordinates for S will be:
x = -4 + 4 = 0
y = 4 - 1 = 3

So, the final coordinates for S in �R "S"T " are (0, 3).

For vertex T(0, 4):
The new coordinates for T will be:
x = 0 + 4 = 4
y = 4 - 1 = 3

So, the final coordinates for T in �R "S"T " are (4, 3).

Therefore, the coordinates for the vertices of �R "S"T " are R(1, 3), S(0, 3), and T(4, 3).