Question

Which of the following points could be the initial point of vector v if it has a magnitude of 10 an the terminal point (-1,5)?

Answer 1

Let the initial point of the vector be (x,y). Then the magnitude of the vector v can be written as:

$|v|= \sqrt{ (-1-x)^{2} + (5-y)^{2} }$

The magnitude of vecor v is given to be 10. So we can write:

$10= \sqrt{ (-1-x)^{2} + (5-y)^{2} } \\ \\ 100=(-1-x)^{2} + (5-y)^{2}$

Now from the given options, we have to check which one satisfies the above equation. That point will be the initial point of the vector. 

The point in option d, satisfies the equation.

$100=(-1+7)^{2} +(5+3)^{2} \\ \\ 100=36+64 \\ \\ 100=100$

Thus, the answer to this question is option D