Write the component form of the vector that translates P(4,5) to P'(-3,7)

The component form of the vector is v = -7·i + 2·j

Step-by-step explanation:

The given parameters are;

The coordinates of the initial point = P(4, 5)

The coordinates of the point after the translation by the vector, v = P'(-3, 7)

Therefore, we have;

The horizontal component of the vector, vₓ = (-3) - 4 = -7

The vertical component of the vector, = 7 - 5 = 2

The magnitude of the translation, v = √(² + vₓ²) = √((-7)² + 2²) = √53 ≈ 7.28

Therefore, the component form of the vector, v, is given as follows;

v = vₓ·i + ·j

Substituting the known values of vₓ and gives;

v = -7·i + 2·j

The component form of the vector is v = -7·i + 2·j.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2