In the coordinate plane, pentagon ABCDE has vertices A(7,3), B(9,–3), C(7,–5), D(1,–1), and E(3,5), and pentagon PQRST has vertices P(0,–2), Q(–1,1), R(0,2), S(3,0), and T(2,–3).Select the sequence of transformations that can be applied to ABCDE to show that it is similar to PQRST.a reflection across the x-axis, followed by a translation right 7 and down 1 and a dilation centered at the origin with scale factor 12a reflection across the x-axis, followed by a translation left 7 and up 1 and a dilation centered at the origin with scale factor 2a rotation of 180° centered at the origin, followed by a translation left 7 and up 1 and a dilation centered at the origin with scale factor 2a rotation of 180° centered at the origin, followed by a translation right 7 and down 1 and a dilation centered at the origin with scale factor 12Submit

The correct sequence of transformations is a reflection across the x-axis, followed by a translation left 7 and up 1 and a dilation centered at the origin with scale factor 2.

Here's why:

1. Reflect ABCDE across the x-axis: This changes the sign of the y-coordinates of each point, giving us A'(7,-3), B'(9,3), C'(7,5), D'(1,1), and E'(3,-5).

2. Translate the reflected figure left 7 and up 1: This involves subtracting 7 from the x-coordinates and adding 1 to the y-coordinates, resulting in A''(0,-2), B''(2,4), C''(0,6), D''(-6,2), and E''(-4,-4).

3. Dilate the translated figure by a factor of 1/2, centered at the origin: This involves multiplying the coordinates of each point by 1/2, giving us A'''(0,-1), B'''(1,2), C'''(0,3), D'''(-3,1), and E'''(-2,-2).

Comparing these final coordinates to those of PQRST, we can see that they match, proving that ABCDE is similar to PQRST through the sequence of transformations described.