Question

Write the component form of the vector that translates A(5,8) to A prime (-4,12).

a) (-9, 4)
b) (9, -4)
c) (11, 20)
d) (-11, -20)

Answer 1

To find the vector that translates A(5,8) to A'(-4,12), subtract the coordinates of A from A' to get the x and y components, resulting in the vector (-9, 4), which corresponds to answer choice (a).

Step-by-step explanation:

The student is asking to compute the component form of the vector that translates point A at (5,8) to point A' at (-4,12). To find this, we subtract the coordinates of the starting point A from the coordinates of the ending point A' to find the vector components. This can be done using the following calculation:

Δx = xe - xb
Δy = ye - yb

For the x-coordinate:

Δx = -4 - 5 = -9

And for the y-coordinate:

Δy = 12 - 8 = 4

Therefore, the component form of the vector is (-9, 4), which is answer choice (a).