Transformation T is defined by T (x, y) = [ 6 -3 -2 7 ].

Question

In the xy-plane, the image of point P under the transformation T is (36, 12). What is the x-coordinate of point P?

Answer 1

To find the x-coordinate of point P, we can set up the following equation using the transformation matrix:

[ 6 -3 -2 7 ] * [ x ] = [ 36 ]
[ y ] = [ 12 ]

This equation can be rewritten as:
6x - 3y = 36
-2x + 7y = 12

Now we can solve this system of equations to find the x-coordinate of point P. By multiplying the first equation by 2 and adding it to the second equation, we get:

12x - 6y = 72
-2x + 7y = 12
_____________________
10x = 84

Dividing by 10 on both sides, we get:
x = 8.4

Therefore, the x-coordinate of point P is 8.4.