Question

Describe a similarity transformation that maps △abc to △rst . a(1, 0), b(−2,−1), c(−1,−2) and r(−3, 0), s(6,−3), t(3,−6) put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. one way to map △abc to △rst is a reflection in the line response area followed by a dilation with center (−3, 0) and scale factor k= response area.

Answer 1

To map △ABC to △RST, perform a reflection in the x-axis followed by a dilation with center (−3, 0) and a scale factor of 3. This sequence of transformations preserves the shape of the triangle.

To map △ABC to △RST using a similarity transformation, we can first perform a reflection and then a dilation.

Reflection:

The line of reflection can be the x-axis. This reflects each point across the x-axis, changing the sign of the y-coordinate while keeping the x-coordinate the same. Therefore, the reflection of point A(1, 0) becomes A'(1, 0), the reflection of B(−2, −1) becomes B' (−2, 1), and the reflection of C(−1, −2) becomes C' (−1, 2).

Dilation:

The center of dilation is (−3, 0), and the scale factor is the ratio of corresponding side lengths. To find the scale factor, we can use the distance formula. For example, the distance from R(−3, 0) to S(6, −3) is 9 units, and the distance from A'(1, 0) to B'(−2, 1) after reflection is 3 units. Therefore, the scale factor (k) is 3.

The dilation with a scale factor of 3 and center (−3, 0) transforms A' to R, B' to S, and C' to T.

In conclusion, the similarity transformation involves a reflection in the x-axis followed by a dilation with center (−3, 0) and a scale factor of 3. This sequence of transformations preserves the shape of △ABC while mapping it onto △RST.