Find the component form of the vector that translates P(4,5) to P'. P'(-3, 7) P'(-1,-6)

We start with the point P(4,5) and this is translated to the point P'(a, b).

We want to find the component form of the vector associated with the translation.

For a general translation for a point: P = (p1, p2) to Q = (q1, q2)  the components of the vector will be:

V = < (q1 - p1), (q2 - p2)>

Then, if the points are:

1) P(4, 5) and P'(-3, 7)

The vector is:

V = < (-3 - 4), (7 - 5) > = <-7, 2>

2) P(4, 5) and P'(-1, - 6)

The vector is:

V = < (-1 - 4), (-6 - 5)> = <-5, -11>

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18