ISEE Upper Level Quantitative : How to find a ray

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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Example Questions

Example Question #1 : How To Find A Ray

Which is the greater quantity?

(a) The length of the line segment connecting \displaystyle (0,0) and \displaystyle (a,b)

(b) The length of the line segment connecting \displaystyle (a,0) and \displaystyle (0,b)

Possible Answers:

(a) and (b) are equal.

(a) is greater.

(b) is greater.

It is impossible to tell from the information given.

Correct answer:

(a) and (b) are equal.

Explanation:

(a) The length of the line segment connecting \displaystyle (0,0) and \displaystyle (a,b) is 

\displaystyle \sqrt{(a -0)^{2}+(b -0)^{2} } = \sqrt{a^{2}+b^{2} }.

(b) The length of the line segment connecting \displaystyle (a,0) and \displaystyle (0,b) is 

\displaystyle \sqrt{(a -0)^{2}+(0-b)^{2} } = \sqrt{a^{2}+\left ( - b \right ) ^{2} }= \sqrt{a^{2}+b^{2} }.

The segments have equal length.

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