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# Both the x and y components of a vector are doubled. Which of the following describes what happens to the resulting vector?

a. magnitude increases by the square root of 2

b. magnitude increases by the square root of 2, and the direction changes

c. magnitude increases by 2

d. magnitude increases by 2, and the direction changes

(pls help!!)

### 3 Answers

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- 6 months ago
(x,y) magnitude = sqrt(x^2 + y^2)

(2x, 2y) magnitude = sqrt( (2x)^2 + (2y)^2 ) = sqrt ( 4(x^2 +y^2) ) = sqrt(4)*sqrt(x^2 + y^2)

magnitude = 2*sqrt(x^2 + y^2)

so

c. magnitude increases by 2

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