Determine the coordinates of the vertices of the image of △ABC after a reflection in the line y=−x. A(3, 4)→ A′ ( )
B(3, 2)→ B′ ( )
C(−1, 2)→ C′ ( )

The coordinates of the vertices of the image of △ABC after a reflection in the line y=−x are A'(-4,-3), B'(-2,-3), and C'(-2,1) and this can be determined by using the rules of transformation.

Given :

The triangle ABC is reflected about the line (y = -x).

The following steps can be used in order to determine the coordinates of the vertices of the image of △ABC after a reflection in the line (y = −x):

Step 1 - Let the coordinate be (x,y) so after the reflection about (y = -x) the coordinate becomes (-y,-x).

Step 2 - The coordinate A(3,4) after the reflection about (y = -x) becomes A'(-4,-3).

Step 3 - The coordinate B(3,2) after the reflection about (y = -x) becomes B'(-2,-3).

Step 4 - The coordinate C(-1,2) after the reflection about (y = -x) becomes C'(-2,1).

For more information, refer to the link given below:

link

See below.

Step-by-step explanation:

A(3, 4)→ A′ (-4, -3)

B(3, 2)→ B′ (-2, -3)

C(−1, 2)→ C′ (-2, 1)

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.