How to find a ray

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ISEE Upper Level Quantitative Reasoning › How to find a ray

Questions 1 - 2

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

(a) and (b) are equal.

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

Explanation

(a) The length of the line segment connecting and is

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

(b) The length of the line segment connecting and is

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

The segments have equal length.

Find the distance between and .

$\sqrt{10}$

$\sqrt{5}$

$\sqrt{2}$

Explanation

To find the distance, first remember the distance formula: $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$ . Plug in so that you have: $\sqrt{(1+2)^2+(4-3)^2}$ . Simplify so that you get $\sqrt{3^2+1^2}$ . This yields $\sqrt{10}$ .

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