How to find a ray - ISEE Upper Level: Quantitative Reasoning

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Question

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

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Answer

(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.

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Question

Find the distance between and .

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Answer

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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Question

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

Tap to reveal answer

Answer

(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.

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Question

Find the distance between and .

Tap to reveal answer

Answer

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 $\sqrt{10}$ .

← Didn't Know|Knew It →

Question

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

Tap to reveal answer

Answer

(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.

← Didn't Know|Knew It →

Question

Find the distance between and .

Tap to reveal answer

Answer

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 $\sqrt{10}$ .

← Didn't Know|Knew It →

Question

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

Tap to reveal answer

Answer

(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.

← Didn't Know|Knew It →

Question

Find the distance between and .

Tap to reveal answer

Answer

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 $\sqrt{10}$ .

← Didn't Know|Knew It →

Knew It

How to find a ray - ISEE Upper Level: Quantitative Reasoning

Which is the greater quantity? (a) The length of the line segment connecting and (b) The length of the line segment connecting and

(a) The length of the line segment connecting and is . (b) The length of the line segment connecting and is . The segments have equal length.

Find the distance between and .

To find the distance, first remember the distance formula: . Plug in so that you have: . Simplify so that you get . This yields .

Which is the greater quantity? (a) The length of the line segment connecting and (b) The length of the line segment connecting and

(a) The length of the line segment connecting and is . (b) The length of the line segment connecting and is . The segments have equal length.

Find the distance between and .

To find the distance, first remember the distance formula: . Plug in so that you have: . Simplify so that you get . This yields .

Which is the greater quantity? (a) The length of the line segment connecting and (b) The length of the line segment connecting and

(a) The length of the line segment connecting and is . (b) The length of the line segment connecting and is . The segments have equal length.

Find the distance between and .

To find the distance, first remember the distance formula: . Plug in so that you have: . Simplify so that you get . This yields .

Which is the greater quantity? (a) The length of the line segment connecting and (b) The length of the line segment connecting and

(a) The length of the line segment connecting and is . (b) The length of the line segment connecting and is . The segments have equal length.

Find the distance between and .

To find the distance, first remember the distance formula: . Plug in so that you have: . Simplify so that you get . This yields .

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

(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.

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 $\sqrt{10}$ .

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

(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.

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 $\sqrt{10}$ .

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

(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.

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 $\sqrt{10}$ .

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

(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.

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 $\sqrt{10}$ .