Question

B (−5, 3) B″ ?

C (−1, 3) C″ ?
D (−1, 1) D″ ?


Complete the table to show the locations of A″, B″, C″, and D″ after both transformations.

A) A″ (−2, −3), B″ (0, −3), C″ (0, 1), D″ (−2, 1)

B) A″ (−3, −2), B″ (−3, 0), C″ (1, 0), D″ (1, −2)

C) A″ (3, 0), B″ (3, 2), C″ (−1, 2), D″ (−1, 0)

D) A″ (3, 2), B″ (3, 0), C″ (−1, 0), D″ (−1, 2)

Answer 1

D) A″ (3, 2), B″ (3, 0), C″ (−1, 0), D″ (−1, 2)

Explanation:

You want the coordinates of points A", B", C", D" after A(-5, 1), B(-5, 3), C(-1, 3), and D(-1, 1) have been translated by <2, -3> and reflected across the origin.

Translation

The translation transformation is given in the problem statement:

(x, y) ⇒ (x +2, y -3)

Reflection

The reflection transformation is ...

(x, y) ⇒ (-x, -y) . . . . . . . reflection across the origin

Composition

The composition of these transformations is ...

(x, y) ⇒ (-(x +2), -(y -3))

(x, y) ⇒ (-x-2, -y+3)

Application

Using this transformation on the given points, we find ...

A(-5, 1) ⇒ A"(-(-5)-2, -1+3) = A"(3, 2)

B(-5, 3) ⇒ B"(-(-5)-2, -3+3) = B"(3, 0)

C(-1, 3) ⇒ C"(-(-1)-2, -3+3) = C"(-1, 0)

D(-1, 1) ⇒ D"(-(-1)-2, -1+3) = D"(-1, 2)