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.

7 0

3 years ago

How much would it have rained each month if the total amount rain (11 inches) was redistributed equally among the 12 moths of th

Colt1911 [192]

Answer:

Total rainfall in one month $0.9167$ inches