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# Starting from point O on a flat school playground, a child walks 10 y

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Joined: 20 Mar 2015
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Starting from point O on a flat school playground, a child walks 10 y  [#permalink]

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18 Jun 2016, 07:10
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Difficulty:

5% (low)

Question Stats:

85% (00:56) correct 15% (01:23) wrong based on 98 sessions

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Starting from point O on a flat school playground, a child walks 10 yards due north, then 6 yards due east, and then 2 yards due south, arriving at point P. How far apart, in yards, are points O and P?

(A) 18
(B) 16
(C) 14
(D) 12
(E) 10

Let point O be the origin.

moving 10 yards due north = (0,10).
moving 6 yards due east = (6,10).
moving 2 yards due south = (6,8) =Final point P.

The distance from origin O(0,0) to point P(6,8) = 10.

Even though I did it in this way, the best way is to not use the coordinates.
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Joined: 02 Aug 2009
Posts: 6785
Re: Starting from point O on a flat school playground, a child walks 10 y  [#permalink]

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18 Jun 2016, 07:39
bimalr9 wrote:
Starting from point O on a flat school playground, a child walks 10 yards due north, then 6 yards due east, and then 2 yards due south, arriving at point P. How far apart, in yards, are points O and P?

(A) 18
(B) 16
(C) 14
(D) 12
(E) 10

Work on the movement in east-west and north south Direction as all moves will be at 90 degree and finally we will have a Right angle triangle..
N-S = 10 UP and 2 down = 10-2 = 8....
E-W = 6..
HYP = $$\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10$$
E
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Re: Starting from point O on a flat school playground, a child walks 10 y  [#permalink]

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19 Jun 2016, 07:59
bimalr9 wrote:
Starting from point O on a flat school playground, a child walks 10 yards due north, then 6 yards due east, and then 2 yards due south, arriving at point P. How far apart, in yards, are points O and P?

(A) 18
(B) 16
(C) 14
(D) 12
(E) 10

Attachment:

Distance.png [ 3.29 KiB | Viewed 3121 times ]

Distance OP = $$\sqrt{8^2 + 6^2}$$ =>10

Hence answer will be (E) 10

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Starting from point O on a flat school playground, a child walks 10 ya  [#permalink]

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05 Oct 2017, 08:04
Starting from point O on a flat school playground, a child walks 10 yards due north, then 6 yards due east, and then 2 yards due south, arriving at point P. How far apart, in yards, are points O and P?

(A) 18
(B) 16
(C) 14
(D) 12
(E) 10
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Posts: 1972
Starting from point O on a flat school playground, a child walks 10 ya  [#permalink]

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05 Oct 2017, 10:14
Bunuel wrote:
Starting from point O on a flat school playground, a child walks 10 yards due north, then 6 yards due east, and then 2 yards due south, arriving at point P. How far apart, in yards, are points O and P?

(A) 18
(B) 16
(C) 14
(D) 12
(E) 10

Attachment:

iiiiii.png [ 5.51 KiB | Viewed 597 times ]

The distance in yards between points O and P is 10

The child creates a trapezoid with her walking pattern. The trapezoid can be divided into a rectangle and a right triangle

1) Find shape created by walking pattern. It will contain right angles (with compass points, "due [any direction]" = 90 degrees)

She walks 10 yards due north from point O to point A: OA = 10

Then 6 yards due east from A to B, which means a right angle at A. AB = 6

Then 2 yards due south from B to P. Another right angle. BP = 2

Connect P to O. She has created a trapezoid with her travel

2) Divide the shape into other shapes where distance between start and finish is easy to calculate

Draw a line from P, PX on diagram, that is perpendicular to OA
The new line divides trapezoid into two new shapes. Upper region is a rectangle. Lower region is right triangle

Rectangle has length = 6, width = 2

The rectangle's width, BP = AX = 2, divides original OA = 10 into two lengths AX and OX:
(OA - AX) = OX
(10 - 2) = 8 = OX

Looking at leg lengths PX and OX: the bottom portion is a 3-4-5 right triangle

3) Find distance between begin and end point

Find length of hypotenuse OP
Rule: If a right triangle has two legs in ratio 3x:4x, it is a 3x-4x-5x triangle and the hypotenuse = 5x

Leg PX = 6
Leg OX = (10 - 2) = 8

(3x: 4x: 5x) = (6: 8: 10)*

Distance between points O and P, in yards: 10

*Or use Pythagorean theorem:
$$6^2 + 8^2 = OP^2$$
$$36 + 64 = OP^2$$
$$100 = OP^2$$
$$OP = 10$$
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Re: Starting from point O on a flat school playground, a child walks 10 y  [#permalink]

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17 Jun 2018, 08:59
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Re: Starting from point O on a flat school playground, a child walks 10 y &nbs [#permalink] 17 Jun 2018, 08:59
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