Question

Which of the following points could be the initial point of vector v if it has a magnitude of 10 and the terminal point (-2,4)?

a. (-0.2, 0.4)
b. (-8, -4)
c. (-12, -6)
d. (1, 3)

Answer 1

Use the distance formula;
10=√(-2-x)²+(4-y)²
Now put the options one by one into the above equation;
you find that option b satisfies the equation which is the correct answer.

Answer 2

Answer:

The initial point is (-8, -4)

Step-by-step explanation:

Given that the terminal point is (-2,4) and the magnitude of vector v is 10 then we have to find the initial point.

Let the initial point is (x, y).

$\text{By distance formula, the length of line joining the points }(x_1,y_1)\text{ and }(x_2, y_2)$

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$10=\sqrt{(-2-x)^2+(4-y)^2}$

The point which satisfy the above condition is the initial point

Option a: (-0.2, 0.4)

$10=\sqrt{(-2-(-0.2))^2+(4-0.4)^2}=\sqrt{3.24+12.96}=\sqrt{16.2}=4.02$

Not satisfied

Option b: (-8, -4)

$10=\sqrt{(-2-(-8))^2+(4-(-4))^2}=\sqrt{36+64}=\sqrt{100}=10$

Satisfied

Option c: (-12, -6)

$10=\sqrt{(-2-(-12))^2+(4-(-6))^2}=\sqrt{100+100}=\sqrt{200}=14.1$

Not satisfied

Option d: (1, 3)

$10=\sqrt{(-2-1)^2+(4-3)^2}=\sqrt{9+1}=\sqrt{10}=3.2$

Not satisfied

Hence, option 2 is correct.

The initial point is (-8, -4)