Triangle xyz has coordinates x(2, 4), y(−3, 4), and z(−3, 1). if the triangle is translated using the rule (x, y) → (x − 2, y + 1), what are the coordinates of y'?

y'(–5, 5)
y'(0, 5)
y'(–5, 2)
y'(–1, 3

Y(−3, 4) is the original

(x, y) → (x − 2, y + 1) is the rule you're using

(-3, 4) → (-3 - 2, 4 + 1)

(-3, 4) → (-5, 5)

Y'(–5, 5)

 The correct option is (A) Y'(-5, 5).

Step-by-step explanation:  Given that the triangle XYZ has coordinates X(2, 4), Y(−3, 4), and Z(−3, 1). The triangle is translated using the following rule :

(x, y)  →  (x − 2, y + 1).

We are to find the co-ordinates of Y'.

The co-ordinates of Y' can be found out by substituting (x, y) = (-3, 4) in the given transformation rule.

Therefore, the co-ordinates of Y' are given by

(-3, 4)  →  (-3 − 2, 4 + 1) = (-5, 5).

Thus, the co-ordinates of Y' are (-5, 5).

Option (A) is CORRECT.

To find the area of the figure you first have to split them up. To find the area for the triangle do 30 x 34 x 16= 16320
Then you find the area of the other shape:
30 x 30 x 16 x 40 = 576000
Then you add them together to get the
576000+16320=592320
So, the answer is 592,320

I hope this helps:)