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ΔTOY has coordinates T (−3, 4), O (−4, 1), and Y (−2, 3). A translation maps point T to T' (−1, 1). Find the coordinates of O' and Y' under this translation.


O' (−2, −2); Y' (0, 0)

O' (−1, −1); Y' (1, 1)

O' (0, 0); Y' (−2, −2)

O' (1, 1); Y' (−1, 0)

Verified Answer :

Given:
T (-3,4) ; O (-4,1) ; Y (-2,3)
T'(-1,1) ; 

T
-3 move forward 2 points to reach -1
4 move forward 3 points to reach 1

O
-4 move forward 2 points to reach -2
1 move forward 3 points to reach -2

Y
-2 move forward 2 points to reach 0
3 move forward 3 points to reach 0.

O'(-2,-2) ; Y'(0,0)   1st option.

Answer:  The correct option is (A) O' (−2, −2); Y' (0, 0).

Step-by-step explanation:  Given that the co-ordinates of the vertices of ΔTOY are T(−3, 4), O (−4, 1), and Y (−2, 3). A translation maps point T to T' (−1, 1).

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

The given transformation from T to T' is

T(−3, 4)   ⇒   T' (−1, 1).

Let,  (−3 + x, 4 + y) =  (-1, 1).

So,

\(-3+x=-1\\\\\Rightarrow x=2\)

and

\(4+y=1\\\\\Rightarrow y=-3.\)

That is, the transformation rule is

(a, b) ⇒ (a+2, b-3).

Therefore,

co-ordinates of O' are (-4+2, 1-3) = (-2, -2),

and

co-ordinates of Y' are (-2+2, 3-3) = (0, 0).

Thus, the required co-ordinates of O' and Y' are (-2, -2) and (0, 0) respectively.

Option (A) is correct.