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.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

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step-by-step explanation: