Question

Describe a similarity transformation that maps AABC to ARST

A(6, 4), B(-2, 0), C(-4, 2) and R(2, 3), S(0,-1), T(1,-2)
One way to map AABC to ARST is a dilation with center at the origin and scale factor
k = _____followed by a reflection in the line_____
a. 1/2
b. 2
c. 3
d. x=1
e. y=-1
f. y=1
g. y=x

Answer 1

A similarity transformation that maps triangle ABC to triangle RST is a dilation with center at the origin and scale factor k = 1/2 followed by a reflection in the line y=x.

Step-by-step explanation:

The question asks to describe a similarity transformation that maps triangle ABC to triangle RST with the given coordinates. To determine the appropriate similarity transformation, we'll need to consider transformations that include dilations (scaling) and reflections.

Firstly, looking at the coordinates given for A(6, 4) and R(2, 3), we can see that if we apply a dilation with a scale factor k = 1/2, point A would be scaled down to A'(3, 2). However, this does not match exactly with point R(2, 3). Similarly, for the other points, a simple dilation would not suffice to map the points from one triangle to the other.

Therefore, we should look for a combination of transformations. The second transformation could be a reflection over a line. Noticing that the y-coordinates of B' and S, as well as C' and T, would match if a reflection over the line y=x were performed after the dilation by 1/2. Hence, this reflects the x and y coordinates over the line y=x, effectively swapping them.

The correct answer is: a dilation with center at the origin and scale factor k = 1/2 followed by a reflection in the line y=x.