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ISEE Lower Level Math : How to find length of a line

Study concepts, example questions & explanations for ISEE Lower Level Math

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All ISEE Lower Level Math Resources

10 Diagnostic Tests 170 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Lines

What is the distance between (2,5) and (-7, 17) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is $d=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$ .

Let $P_{1}=(-7,17)$ and $P_{2}=(2,5)$ :

$d=\sqrt{(2-(-7))^{2} + (5-17)^{2}}=\sqrt{(9)^{2} + (-12)^{2}}=\sqrt{81 + 144}=\sqrt{225}=15$

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Example Question #2 : Lines

What is the distance between (-2, 3) and (4, -5) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is given by $d=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$ .

Let $P_{1}=(4,-5)$ and $P_{2}=(-2,3)$ :

$d=\sqrt{(-2-4)^{2} + (3-(-5)^{2}}=\sqrt{(-6)^{2} + (8)^{2}}=\sqrt{36 + 64}=\sqrt{100}=10$

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Example Question #3 : Lines

What is the distance between (1,-3) and (13,-8) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is given by $d=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$ .

Let $P_{1}=(1,-3)$ and $P_{2}=(13,-8)$ :

$d=\sqrt{(13-1)^{2} + (-8-(-3)^{2}}=\sqrt{(12)^{2} + (-5)^{2}}=\sqrt{144 + 25}=\sqrt{169}=13$

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Example Question #4 : Lines

What is the distance between the points (-2,1) and (10,-4) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is $d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ .

Let $P_{1}= (-2, 1)$ and $P_{2}=(10, -4)$ .

Plug these two points into the distance formula:

$d = \sqrt{(10-(-2))^{2}+(-4-1)^{2}}=\sqrt{(12)^{2}+(-5)^{2}}=\sqrt{144+25}=\sqrt{169}=13$

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Example Question #5 : Lines

If a line with a length of 5 starts at the point (1,1) , which of the following is NOT a possible end point?

Possible Answers:

(-3, 4)

(5, -2)

(-2, -3)

(-3,5)

(4, 5)

Correct answer:

(-3,5)

Explanation:

Let $P_{1}=(1,1)$ , and let $P_{2}$ be the end point we are looking for.

Recall the distance formula:

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

Squaring the distance formula gives $d^{2} = (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$ .

Plug $P_{1}=(1,1)$ this squared distance formula and solve for $P_{2}$ :

$25 = (x_{2}-1)^{2}+(y_{2}-1)^{2}$

Substitute each response into this equation to see which one is false. The only response that doesn't work is (-3, 5) .

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Example Question #401 : Geometry

What is the distance between (-2, 1) and (1,5) ?

Possible Answers:

Correct answer:

Explanation:

The distance formula is $d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ .

Let $P_{1}= (-2, 1)$ and $P_{2}=(1, 5)$ .

Plug these points into the distance formula:

$d = \sqrt{(1-(-2))^{2}+(5-1)^{2}}=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}=5$

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Example Question #6 : How To Find Length Of A Line

If a line that is 13 inches in length starts at the point (1,2) , which of the following is NOT a possible end point?

Possible Answers:

(3, 15)

(6, 14)

(-4, -10)

(-11, -3)

(13, 7)

Correct answer:

(3, 15)

Explanation:

The distance formula is given by $d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ .

Square both sides:

$d^{2} = (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$

Now, let $P_{1}=(1,2)$ , and let $P_{2}$ be the end point we are looking for.

Plug $P_{1}=(1,2)$ into the squared distance formula and solve for $P_{2}$ :

$169 = (x_{2}-1)^{2}+(y_{2}-2)^{2}$

Alternatively, you can plug in the answer choices and see which point makes the above equation untrue. The point (3, 15) matches this description and is therefore the correct answer.

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Example Question #3 : How To Find Length Of A Line

How long is a line segment on the number line if it goes from to ?

Possible Answers:

Correct answer:

Explanation:

To find the length of a line on the number line when one point is negative and the other is positive, you must the the distances of both from zero. is spaces from zero where is the other point is just . So the distance is 6+5=11 .

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Example Question #2 : How To Find Length Of A Line

What is the distance between (2,5) and (-7, 17)?

Possible Answers:

Correct answer:

Explanation:

The distance formula is $d=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$ .

Let $P_{1}=(-7,17)$ and $P_{2}=(2,5)$ :

$d=\sqrt{(2-(-7))^{2} + (5-17)^{2}}=\sqrt{(9)^{2} + (-12)^{2}}=\sqrt{81 + 144}=\sqrt{225}=15$

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All ISEE Lower Level Math Resources

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ISEE Lower Level Math : How to find length of a line

Study concepts, example questions & explanations for ISEE Lower Level Math

All ISEE Lower Level Math Resources

Example Questions

Example Question #1 : Lines

Example Question #2 : Lines

Example Question #3 : Lines

Example Question #4 : Lines

Example Question #5 : Lines

Example Question #401 : Geometry

Example Question #6 : How To Find Length Of A Line

Example Question #3 : How To Find Length Of A Line

Example Question #2 : How To Find Length Of A Line

All ISEE Lower Level Math Resources

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