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Mark and Kim are at the post office. To get home, Kim walks 3 miles no

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Mark and Kim are at the post office. To get home, Kim walks 3 miles no  [#permalink]

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New post 25 Feb 2019, 02:28
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Mark and Kim are at the post office. To get home, Kim walks 3 miles north and 2 miles west and Mark walks 8 miles south and 2 miles east. What is the approximate straight-line distance between Kim’s house and Mark’s house?

A. 10.1 miles
B. 11.7 miles
C. 12 miles
D. 13.2 miles
E. 15 miles

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Mark and Kim are at the post office. To get home, Kim walks 3 miles no  [#permalink]

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New post Updated on: 26 Feb 2019, 00:51
Bunuel wrote:
Mark and Kim are at the post office. To get home, Kim walks 3 miles north and 2 miles west and Mark walks 8 miles south and 2 miles east. What is the approximate straight-line distance between Kim’s house and Mark’s house?

A. 10.1 miles
B. 11.7 miles
C. 12 miles
D. 13.2 miles
E. 15 miles


plot values
we get
√(11^2 +4^2) = ~ 11.7 miles
IMO B
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Originally posted by Archit3110 on 25 Feb 2019, 04:24.
Last edited by Archit3110 on 26 Feb 2019, 00:51, edited 2 times in total.
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Re: Mark and Kim are at the post office. To get home, Kim walks 3 miles no  [#permalink]

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New post 25 Feb 2019, 23:57

Solution


Given:
    • Mark and Kim are at the post office.
    • To get home, Kim walks 3 miles north and 2 miles west and Mark walks 8 miles south and 2 miles east.

To find:
    • The approximate straight-line distance between Kim’s house and Mark’s house

Approach and Working:

Image

The figure represents the final position of Kim and Mark.
    • Therefore, the approximate straight-line distance = \(\sqrt{4^2 + 11^2} = \sqrt{137}\) = 11.7 miles

Hence, the correct answer is option B.

Answer: B

Image

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Re: Mark and Kim are at the post office. To get home, Kim walks 3 miles no  [#permalink]

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New post 01 Mar 2019, 11:01
Bunuel wrote:
Mark and Kim are at the post office. To get home, Kim walks 3 miles north and 2 miles west and Mark walks 8 miles south and 2 miles east. What is the approximate straight-line distance between Kim’s house and Mark’s house?

A. 10.1 miles
B. 11.7 miles
C. 12 miles
D. 13.2 miles
E. 15 miles


We can place the post office at the origin (0, 0) on the coordinate plane. Thus, Kim’s house would be at the point (-2, 3), and Mark’s house would be at the point (2, -8). Using the distance formula, we see that the distance between their houses is:

√[(-2 -2)^2 + (3 - (-8))^2] = √[(-4)^2 + 11^2] = √[16 + 121] = √137 ≈ 11.7

Answer: B
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Re: Mark and Kim are at the post office. To get home, Kim walks 3 miles no   [#permalink] 01 Mar 2019, 11:01
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