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In the xy plane, the vertices of a triangle have coordinates
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monirjewel
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In the xy-plane, the vertices of a triangle have coordinates (0,0),(3, [#permalink] New post  Updated on: 31 Oct 2016, 22:23
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In the xy-plane, the vertices of a triangle have coordinates (0,0),(3,3), and (7,0). What is the perimeter of the triangle?

(A) 13
(B) (14)
(C) (16)
(D) (17)
(E) 12+3 root 2

How to draw graph on this?
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Originally posted by monirjewel on 28 Oct 2010, 21:18.
Last edited by Bunuel on 31 Oct 2016, 22:23, edited 1 time in total.
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Bunuel
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Re: In the xy plane, the vertices [#permalink] New post  05 Nov 2010, 20:08
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monirjewel wrote:
In the xy plane, the vertices of a triangle have coordinates(0,0), (3,3), and (7,0). What is the perimeter of the triangle?
(A) 13
(B) 34
(C) root 43
(d) 7+root3
(E) 12 +3root2


The formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).

Distance between (0, 0) and (7, 0) is \(d=7\);
Distance between (0, 0) and (3, 3) is \(d=\sqrt{(0-3)^2+(0-3)^2}=\sqrt{18}=3\sqrt{2}\);
Distance between (3, 3) and (7, 0) is \(d=\sqrt{(3-7)^2+(3-0)^2}=5\);

\(P=7+3\sqrt{2}+5=12+3\sqrt{2}\).

Answer: E.

For more check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
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Re: In the xy-plane, the vertices of a triangle have coordinates (0,0),(3, [#permalink] New post  28 Oct 2010, 23:27
Moving to PS sub-forum ...


!
Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/


To answer this question ... all you need is distance between vertices :

(0,0) & (7,0) : 7
(0,0) & (3,3) : \(3\sqrt{2}\)
(7,0) & (3,3) : \(\sqrt{16+9}=5\)

Perimeter = sum of these three sides = \(12 + 3\sqrt{2}\)

Answer : e
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In the xy plane, the vertices of a triangle have coordinates [#permalink] New post  05 Nov 2010, 19:31
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In the xy plane, the vertices of a triangle have coordinates(0,0), (3,3), and (7,0). What is the perimeter of the triangle?

(A) 13
(B) 34
(C) root 43
(D) 7+root3
(E) 12 +3root2
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Re: In the xy plane, the vertices [#permalink] New post  03 Jan 2013, 03:10
monirjewel wrote:
In the xy plane, the vertices of a triangle have coordinates(0,0), (3,3), and (7,0). What is the perimeter of the triangle?
(A) 13
(B) 34
(C) root 43
(d) 7+root3
(E) 12 +3root2


Get distance between (0,0) and (3,3): \(\sqrt{(3 - 0)^2 + (3-0)^2} = \sqrt{(18)} = 3 \sqrt{(2)}\)
Get distance between (3,3) and (7,0): \(\sqrt{(7-3)^2 + (3-0)^2} = \sqrt{16 + 9}= \sqrt{25}=5\)
Get distance between (0,0) and (7,0): 7

\(P = 7 + 5 + 3\sqrt{2} = 12 + \sqrt{2}\)

Answer: E
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Re: In the xy plane, the vertices of a triangle have coordinates [#permalink] New post  31 Jul 2016, 01:15
Hi Bunnuel,

Is there any formula to calculate area of triangle when all coordinates are known?

Please help. Many thanks in advance for your kind response

Regards
Megha
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Re: In the xy plane, the vertices of a triangle have coordinates [#permalink] New post  31 Jul 2016, 01:25
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megha_2709 wrote:
Hi Bunnuel,

Is there any formula to calculate area of triangle when all coordinates are known?

Please help. Many thanks in advance for your kind response

Regards
Megha


I really doubt that you'll need it for the GMAT but here you go:

If the vertices of a triangle are: \(A(a_x, a_y)\), \(B(b_x, b_y)\) and \(C(c_x,c_y)\) then the area of ABC is:

\(area=|\frac{a_x(b_y-c_y)+b_x(c_y-a_y)+c_x(a_y-b_y)}{2}|\).
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Re: In the xy plane, the vertices of a triangle have coordinates [#permalink] New post  01 Aug 2016, 12:42
Bunuel wrote:
megha_2709 wrote:
Hi Bunnuel,

Is there any formula to calculate area of triangle when all coordinates are known?

Please help. Many thanks in advance for your kind response

Regards
Megha


I really doubt that you'll need it for the GMAT but here you go:

If the vertices of a triangle are: \(A(a_x, a_y)\), \(B(b_x, b_y)\) and \(C(c_x,c_y)\) then the area of ABC is:

\(area=|\frac{a_x(b_y-c_y)+b_x(c_y-a_y)+c_x(a_y-b_y)}{2}|\).



Ohh,

A day before I saw question like that on gmat club. Anyways many thanks for your response and telling me its highly unlikely to come. :)

Regards
Megha
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Re: In the xy-plane, the vertices of a triangle have coordinates (0,0),(3, [#permalink] New post  31 Oct 2016, 16:09
Relatively straight-forward problem, though I'd suggest plotting it so you can visualize the sides and what two side lengths you will need to calculate.

Base length is 7

(1) Distance between (0,0) & (3,3) --> sqrt[(3^2)+(3^2)] = 3sqrt(2)

(2) Distance between (3,3) & (7,0) --> sqrt[(3-0)^2 + (3-7)^2] = sqrt(9+16) = sqrt(25) =5

Add them all up --> 12+ 3sqrt(2)

E
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Re: In the xy plane, the vertices of a triangle have coordinates [#permalink] New post  14 Nov 2016, 06:09
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monirjewel wrote:
In the xy-plane, the vertices of a triangle have coordinates (0,0),(3,3), and (7,0). What is the perimeter of the triangle?

(A) 13
(B) (14)
(C) (16)
(D) (17)
(E) 12+3 root 2

How to draw graph on this?


Plot the graph and you will get two triangles one is pythagorean triples(3, 4, 5) and 3, 3, and 3sqrt(2)

by this perimeter is 12+3sqrt(2)
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Re: In the xy plane, the vertices of a triangle have coordinates [#permalink] New post  26 May 2020, 23:04
An efficient way of solving this problem is by recalling common sides of a triangle.

- We know that the length of one of the sides is 7 simply because it's the distance between coordinates (0,0) and (7,0).

- We can split the triangle into 2 smaller triangles
--> Triangle 1 coordinates (0,0), (3,3) and (3,0)
--> Triangle 2 coordinates (3,0), (3,3) and (7,0)

- Triangle 1 has sides that appear to be very similar to the common triangle with sides (1):(1):(√2). In fact, its sides can be written as (3):(3):(3√2) and now we know that one side of the original triangle is (3√2).

- Triangle 2 has sides that are exactly the same as the common triangle with sides (3):(4):(5) and now we know that one side of the original triangle is (5).


Our perimeter is (7) + (3√2) + (5) = 12 +3√2

Looking at the answer choices, we can also tell that the only answer choice that contains (3√2) is answer choice E
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Re: In the xy plane, the vertices of a triangle have coordinates [#permalink]
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