Question

After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(6, 3), B'(–2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image?
A -

B -

C -

Answer 1

Given coordinates of the transformed image:

A'(6, 3),

B'(–2, 1), and

C'(1, 7).

We need to find the coordinates of the pre-image A, B and C.

The rule for rotation of 90° about the origin is (x,y) ---> (-y,x).

But we need to find the coordinates of the vertices of the pre-image.

So, we need to apply rule (-y,x) ---->(x,y).

Applying rule,

A'(6, 3) -----> A (3, -6)

B'(–2, 1) -----> B(1, 2)

C'(1,7) -----> C (7, -1).

Therefore, coordinates of the vertices of the pre-image are

A (3, -6)

B(1, 2)

C (7, -1).

Answer 2

Answer:

A (3,-6)

B(1,2)

C(7,-1)

Step-by-step explanation:

We are given that after rotation of 90 degerees about the origin, the coordinates of the vertices of the image of a triangle are A'(6,3),B'(-2,1) and C'(1,7).

We have to find the coordinates of the vertices of the pre-image.

We know that the translation rule when a figure rotate 90 degrees about the origin is given by

$(x,y)\rightarrow (-y,x)$

We have to find the vertices of pre- image therefore we apply

$(-y,x)\rightarrow (x,y)$

Now, using this rule , then we get

Th vertex of A is given by

$(6,3)\rightarrow (3,-6)$

The vertex of B is given by

$(-2,1)\rightarrow (1,2)$

The vertex of C is given by

$(1,7)\rightarrow (7,-1)$