If coordinates (−2,−5) undergo a translation vector of <2,−3> in the coordinate plane, what would the resulting coordinates be?(1 point)

Question

Responses which answer is correct a b c or d

(4,2)
left parenthesis 4 comma 2 right parenthesis

(4,−2)
left parenthesis 4 comma negative 2 right parenthesis

(0,−2)
left parenthesis 0 comma negative 2 right parenthesis

(0,−8)

Answer 1

To find the new coordinates after the translation, we add the components of the translation vector to the corresponding coordinates of the original point.

Original coordinates: \((-2, -5)\)
Translation vector: \(\langle 2, -3 \rangle\)

Now, we perform the translation:

• New x-coordinate = original x-coordinate + translation x-component
  \(-2 + 2 = 0\)

• New y-coordinate = original y-coordinate + translation y-component
  \(-5 + (-3) = -5 - 3 = -8\)

So, the resulting coordinates after the translation will be \((0, -8)\).

Therefore, the correct answer is:

(0, −8)