I'm completely stuck on this, I need a full explanation and solution. It's about matrices

Question

A translation of triangle ABC can be represented by the following matrix equation where B has the coordinates (a, b) and C’ has the coordinates (c, d). (i cant attach an image so ill try to write the matrix equation, it looks a bit weird)

[-3 a 2 ] [x x x] [4 3 c]

+ =

[2 b -1] [y y y] [7 0 d]

Describe the translation by circling each choice and filling in each blank

-Left/Right _____ units.

-Up/Down ______ units.

Use the equation to determine the following coordinates:

B _____

C _____

Answer 1

Comparing the first columns of the leftmost and rightmost matrices, A = (-3,2) is translated to A' = (4,7).

So, A is translated 7 units to the right and 5 units upward.This means that x = 7 and y = 5. Also, B and C and all other points of ΔABC are translated in the same manner. Under the translation, A, B, and C move to A', B', and C' respectively.

a + 7 = 3 So, a = -4

2 + 7 = c So, c = 9

b + 5 = 0 So, b = -5

-1 + 5 = d So d = 4

B = (a, b) = (-4, -5) and C' = (c, d) = (9, 4).