Question

Translate quadrilateral PQRS 2 units to the left and 5 units down. What are the coordinates of the vertices of the image? A. P'(-6, -2), Q'(2, -3), R'(1, -9), and S'(-5, -11) B. P'(-2, -6), Q'(2, -3), R'(-9, -1), S'(5, -11) C. P'(-6, -2), Q'(-3, -2), R'(-1, -9), and S'(-11, -5) D. P'(6, -2), Q'(2, 3), R'(1, -9), and S'(-5, 11)

Answer 1

The coordinates after translating PQRS 2 units left and 5 units down are: P'(-6, -2), Q'(-3, -2), R'(-1, -9), and S'(-11, -5), matching option C. Thus the correct option is C. P'(-6, -2), Q'(-3, -2), R'(-1, -9), and S'(-11, -5)

Step-by-step explanation:

To translate the quadrilateral PQRS 2 units to the left and 5 units down, subtract 2 from the x-coordinates and 5 from the y-coordinates of the original vertices.

The coordinates of the vertices after translation are: P'(-6, -2), Q'(-3, -2), R'(-1, -9), and S'(-11, -5).

To find the new coordinates after the translation, subtract 2 from the x-coordinates of P, Q, R, and S, and subtract 5 from their y-coordinates:

P(-4, 3) → P'(-4 - 2, 3 - 5) → P'(-6, -2)

Q(0, 3) → Q'(0 - 2, 3 - 5) → Q'(-2, -2)

R(2, 0) → R'(2 - 2, 0 - 5) → R'(-1, -5)

S(-2, 0) → S'(-2 - 2, 0 - 5) → S'(-4, -5)

Therefore, the translated coordinates are P'(-6, -2), Q'(-3, -2), R'(-1, -9), and S'(-11, -5). This corresponds to option C. Thus the correct option is C. P'(-6, -2), Q'(-3, -2), R'(-1, -9), and S'(-11, -5).

Answer 2

So, the correct answer is option
`A: \(P'(-6, -2), Q'(2, -3), R'(1, -9),\) and \(S'(-5, -11)\)`.

To translate a figure, you can simply add or subtract values from the coordinates of its vertices. In this case, you need to move the quadrilateral
`\(PQRS\)` 2 units to the left (subtract 2 from the x-coordinates) and 5 units down (subtract 5 from the y-coordinates).

Let's apply this translation to each vertex:

- Vertex
`\(P'(-6, -2)\)`: Subtract 2 from the x-coordinate of P and 5 from the y-coordinate of P.

- Vertex
`\(Q'(2, -3)\)`: Subtract 2 from the x-coordinate of Q and 5 from the y-coordinate of Q.

- Vertex
`\(R'(1, -9)\)`: Subtract 2 from the x-coordinate of R and 5 from the y-coordinate of R.

- Vertex
`\(S'(-5, -11)\)`: Subtract 2 from the x-coordinate of S and 5 from the y-coordinate of S.

Complete the image: