If coordinates (-4, 7) undergo a translation vector of <-4,8> in the coordinate plane, what would the resulting coordinated be?

Question

a. (-8, 15)
b. (-8, -1)
c. (8, -15)
d. (0, -1)

Answer 1

To find the resulting coordinates after applying the translation vector <-4, 8> to the original coordinates (-4, 7), we need to add the components of the translation vector to the corresponding components of the original coordinates.

The original coordinates are:

• \(x = -4\)
• \(y = 7\)

The translation vector components are:

• \(x\) component = -4
• \(y\) component = 8

Now, we calculate the new coordinates:

• New \(x\) coordinate: \[ -4 + (-4) = -4 - 4 = -8 \]
• New \(y\) coordinate: \[ 7 + 8 = 15 \]

Therefore, the resulting coordinates after the translation are \((-8, 15)\).

The correct answer is: a. (-8, 15)