Use the image to answer the question.

Question

A rectangle is labeled clockwise from the upper right upper A upper B upper D upper C. The area inside of the rectangle is shaded, and each of the vertices is labeled.

Destinee wants to translate rectangle ABDC
horizontally by −5
and vertically by +5 to produce rectangle A′B′D′C′
. Which of the following options shows the correct coordinates of C′
after this translation?

(1 point)
Responses

(0,−4)
left parenthesis 0 comma negative 4right parenthesis

(−10,6)
left parenthesis negative 10 comma 6 right parenthesis

(−10,−4)
left parenthesis negative 10 comma negative 4 right parenthesis

(0,6)

Answer 1

To determine the new coordinates of point C′ after translating point C by −5 horizontally and +5 vertically, we first need the original coordinates of point C.

Assuming the coordinates of point C are (x, y), applying the translations will result in the following new coordinates:

• Horizontal translation by -5: x - 5
• Vertical translation by +5: y + 5

So the new coordinates for C′ will be: C′(x - 5, y + 5)

Now, without the original coordinates of point C, it's not possible to calculate the exact coordinates of C′. However, we can analyze the response options.

If you assume some common coordinates for point C like (−5, 1):

• Translate horizontally: −5 - 5 = −10
• Translate vertically: 1 + 5 = 6 This gives us C′ = (−10, 6).

If C starts with any other coordinates, you'd need to perform the same operation to see which final coordinate matches your translation outcomes based on the responses provided.

Among the options:

• (0, -4)
• (−10, 6)
• (−10, −4)
• (0, 6)

The point (−10, 6) fits if the original coordinates for point C are at (−5, 1).

Thus, assuming the coordinates of C fit with that transformation, the correct option showing the coordinates of C′ after the translation is:

(−10, 6)