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SSAT Upper Level Math : How to find the length of a line with distance formula

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Example Questions

Example Question #112 : Coordinate Geometry

Give the length, in terms of , of a segment on the coordinate plane whose endpoints are (A+2, A-2) and the origin.

Possible Answers:

$\sqrt{ 2A^{2}- 8 }$

$2 \sqrt{2A}$

$\sqrt{ 2A^{2}+ 8A+8 }$

$\sqrt{ 2A^{2}+ 8 }$

$\sqrt{ 2A^{2}- 8A+8 }$

Correct answer:

$\sqrt{ 2A^{2}+ 8 }$

Explanation:

The distance between two points $(x_{1}, x_{2})$ and $(y_{1}, y_{2})$ can be obtained using the formula

$d = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}$

Setting $x_{1}= y_{1} = 0, x_{2}=A+2, y_{2} = A-2$ , we can find our expression:

$d = \sqrt{\left ( \left [A+2 \right )-0\right ]^{2}+\left [\left (A-2 \right )-0 \right ] ^{2}}$ $= \sqrt{\left ( A+2 \right ) ^{2}+ \left (A-2 \right ) ^{2}}$

$= \sqrt{\left ( A^{2}+4A+4 \right )+\left ( A^{2}-4A+4 \right ) }$

$= \sqrt{ 2A^{2}+ 8 }$

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Example Question #111 : Coordinate Geometry

Give the length, in terms of , of a segment on the coordinate plane whose endpoints are (A,A) and (3,3)

Possible Answers:

$\sqrt{2A^{2} +18 }$

$\sqrt{2A^{2}+12A+18 }$

$\sqrt{2A^{2}-12A+18 }$

A - 3

$\sqrt{2A^{2} -18 }$

Correct answer:

$\sqrt{2A^{2}-12A+18 }$

Explanation:

The distance between two points $(x_{1}, x_{2})$ and $(y_{1}, y_{2})$ can be obtained using the formula

$d = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}$

Setting $x_{1}= y_{1} =3, x_{2}= y_{2} = A$ , we can find our expression:

$d = \sqrt{\left (A-3 \right )^{2}+\left (A-3\right )^{2}}$

$= \sqrt{\left (A^{2}-6A+9 \right ) + \left (A^{2}-6A+9 \right ) }$

$= \sqrt{2A^{2}-12A+18 }$

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SSAT Upper Level Math : How to find the length of a line with distance formula

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #112 : Coordinate Geometry

Example Question #111 : Coordinate Geometry

All SSAT Upper Level Math Resources

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