Which sequence of rigid transformations will map the preimage δabc onto image δa′b′c′ ?
a reflection across the x-axis, a translation 8 units right, and then a reflection across the x-axis

a translation 4 units down and 10 units to the right

a reflection across the line y = x followed by a rotation 90° counterclockwise

a rotation 180° clockwise followed by a reflection across the x-axis

Answer-

"A. A reflection across the x-axis, a translation 8 units right, and then a reflection across the x-axis" will produce the desired image.

Solution-

Co-ordinates of the points are,

A = (-4, 2)

B = (-6, 2)

C = (-2, 6)

The reflection of the point (x,y) across  the x-axis is the point (x,-y).

So, new co-ordinates are,

A = (-4, -2)

B = (-6, -2)

C = (-2, -6)

The translation of the point (x,y) by 8 units right is the point (x+8,y).

So, new co-ordinates are,

A = (4, -2)

B = (2, -2)

C = (6, -6)

Again, the reflection of the point (x,y) across  the x-axis is the point (x,-y).

So, new co-ordinates are,

A' = (4, 2)

B' = (2, 2)

C' = (6, 6)

As, these are the co-ordinates of the A'B'C', so the first option is correct.