triangle has vertices A( 0,0 ), B(2, 0) and C(0, 4). Angle ABC is transformed to angle A"B"C" by a rotation of 180 degrees clockwise about the origin, followed by a dilation with the origin as the center of dilation and scale factor of 3. find the coordinates of the vertices of angle A"B"C" and state whether the two triangles are similar or congruent.

Step-by-step explanation:

The pre-image points are A( 0,0 ), B(2, 0) and C(0, 4). The question is asking you to rotate the traingle 180°. Each rotation has its rules. For 180° rotation our rule is (x,y) → (-x,-y). Let's apply that to our points:

A( 0,0 ), → (0,0)

B(2, 0) → (-2,0)

and C(0, 4). → (0,-4)

Now we dilate our point ( remember the order in which you do transformation is important. Since it saids the rotation is followed that means the dilation is done second)

Our scale factor is 3. Remember when our scale factor is more than one our shape gets bigger. So our rule is (x,y) → (kx,ky). Let's apply our scale factor to all our points:

(0,0) → (0,0)

(-2,0)→( -6,0)

(0,-4) → (0,-12)

The answer is

A' (0,0) B' (-6,0) C' (0,-12)

The triangles will be similar not congruent. Remember congruent triangles have the same angles and same sizes. Similar angles have the same angles BUT different sizes. Every transformation produces congruent angles except for dilations.

60: 45 =12: 9 =4: 3 so the answer is 4: 3