Question

point T"(-2,5) is a vertex of triangle T"O"P". The original image was rotated 90° counterclockwise around the origin and rhen translated (x,y)->(×-1,y+7). What are the coordinates of the original image's point T before the composition of transformations?​

Answer 1

The coordinates of point T are:

(-2,1)

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)

Answer 2

T(-2,1)

EXPLANATION

Let T(a,b) be the coordinates.

When this point is rotated 90° counterclockwise about the origin,

Then,

`T(a,b)\to \: T'( - b,a)`

If this point is then translated using the rule;

`(x,y)\to (x-1,y+7)`

then,

`T(a,b)\to \: T'( - b,a) \to T`

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)