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

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 .

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 $\sqrt{10}$ .

Compare your answer with the correct one above

Question

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

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.

Compare your answer with the correct one above

Question

Find the distance between and .

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 $\sqrt{10}$ .

Compare your answer with the correct one above

Question

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

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.

Compare your answer with the correct one above

Question

Find the distance between and .

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 $\sqrt{10}$ .

Compare your answer with the correct one above

Question

Which is the greater quantity?

(a) The length of the line segment connecting and

(b) The length of the line segment connecting and

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.

Compare your answer with the correct one above

Question

Find the distance between and .

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 $\sqrt{10}$ .

Compare your answer with the correct one above

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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 $\sqrt{10}$ .