Question

PLEASE HELP ME

Answer 1

Answer:

• The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.

Explanation:

By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.

You can check that analitically

Departing from the triangle: XYZ

• Translation 5 units to the left: (x,y) → (x - 5, y)

• Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)

• Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)

• Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)

• Translation 1 unit down: (x,y) → (x, y-1)

• (-11,2) → (-11, 2 - 1) = (-11, 1)

• (-9,7) → (-9, 7 - 1) = (-9, 6)

• (-7, 2) → (-7, 2 - 1) = (-7, 1)

• Reflextion accross the x-axis: (x,y) → (x, -y)

• (-11, 1) → (-11, -1), which are the coordinates of vertex X"

• (-9, 6) → (-9, -6), which are the coordinates of vertex Y""

• (-7, 1) → (-7, -1), which are the coordinates of vertex Z"

Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.