ANSWER
T(-2,1)
EXPLANATION
Let T(a,b) be the coordinates.
When this point is rotated 90° counterclockwise about the origin,
Then,
[tex]T(a,b)\to \: T'( - b,a)[/tex]
If this point is then translated using the rule;
[tex](x,y)\to (x-1,y+7)[/tex]
then,
[tex]T(a,b)\to \: T'( - b,a) \to T"( - b - 1,a + 7)[/tex]
It was given that, T"(-2,5)
This implies that,
-b-1=-2
-b=-2+1
-b=-1
b=1
a+7=5
a=5-7
a=-2
Therefore the coordinates of T are:
(-2,1)
Answer:
The coordinates of point T are:
(-2,1)
Step-by-step explanation:
Let us suppose that the actual coordinate of point T be (x,y).
Now when a point is rotated counterclockwise around the origin the rule that holds or this transformation is:
(x,y) → (-y,x)
Hence, T(x,y) → T'(-y,x)
Now again we are applying a transformation by the rule:
(x,y) → (x-1,y+7)
Hence, the point after transformation is:
T'(-y,x) → T"(-y-1,x+7)
As we are given that the Point T" is:
T"(-2,5)
This means that:
(-y-1,x+7)=(-2,5)
⇒ -y-1= -2 and x+7=5
⇒ y=-1+2 and x=5-7
⇒ y=1 and x= -2
Hence, the coordinates of Point T before the transformation is:
(-2,1)
