Triangle abc is transformed to create triangle def. what sequence of transformations maps one to the other? select all that apply.
a.
rotate 180° about the origin, then translate left 2 units
b.
reflect over the x-axis, then translate down 2 units
c.
translate 2 units to the right, then rotate 180° about the origin
d.
translate 2 units to the right, then reflect over the x-axis

B. Reflect over the x-axis, then translate down 2 units

Since we are dealing with rigid transformations (no dilation), both triangles are congruent, which means if point A maps to D and D maps to A after the sequence of transformation, the rest of the points will map as well. So, to prove that a sequence of transformations maps one triangle to the other, we just need to prove A = D and D = A after the transformations.

We can infer from the picture that A = (-4, 2) and D = (-4, -4), so let's apply each of the sequences:

A. - The rule to reflect a point  180° about the origin is (x, y) → (-x, -y). In other words, we change the sign of both coordinates.

- The rule to translate a point 2 units left is (x, y) → (x-2, y). In other words, we subtract 2 from the x-coordinate.

∴ Rotate A 180° about the origin: (x, y) → (-x, -y) = (-4, 2) → (4, -2)

∴ Translate the resulting point 2 units left: (x, y) → (x-2, y) = (4-2, -2) = (2, -2)

The resulting point is not equal D (2, -2) ≠ (-4, -4), so this is not one of our sequences.

B. - The rule to reflect a point over the x-axis is (x, y) → (x, -y). In other words, we change the signs of the y-coordinate.

- The rule to translate a point 2 units down is (x, y) → (x, y-2). We subtract two from the y-coordinate.

∴ Reflect A over the x-axis: (x, y) → (x, -y) = (-4, -2)

∴ Translate the resulting point 2 units down: (x, y) → (x, y-2) = (-4, -2-2) = (-4, -4)

Notice that we end up at D, so lets check if the opposite holds:

∴ Reflect D over the x-axis: (x, y) → (x, -y) =(-4, -4) → (-4, 4)

∴ Translate the resulting point 2 units down: (x, y) → (x, y-2) = (-4, 4-2) = (4, 2)

We end up at A, so after the sequence of transformations A = D and D = A. We can conclude that this sequence of transformations maps one triangle to the other.

C. - The rule to translate a point 2 units right is (x, y) → (x+2, y). In other words, we add 2 from the x-coordinate.

- The rule to reflect a point  180° about the origin is (x, y) → (-x, -y).

∴ Translate A 2 units right: (x, y) → (x+2, y) = (-4+2, 2) = (-2, 2)

∴ Rotate the resulting point  180° about the origin: (x, y) → (-x, -y) = (-2, 2) → (2 , -2)

The resulting point is not equal D (2, -2) ≠ (-4, -4), so this is not one of our sequences.

D. - The rule to translate a point 2 units right is (x, y) → (x+2, y).

- The rule to reflect a point over the x-axis is (x, y) → (x, -y).

∴ Translate A 2 units right: (x, y) → (x+2, y) = (-4+2, 2) = (-2, 2)

∴ Reflect the resulting point  over the x-axis: (x, y) → (x, -y) = (-2, 2) → (-2 , -2)

The resulting point is not equal D (-2, -2) ≠ (-4, -4), so this is not one of our sequences.

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step-by-step explanation:

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )