In the xy plane, the vertices of a triangle have coordinates

Question

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?

Bunuel · Accepted Answer

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.

NandishSS · Answer

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)

shrouded1 · Answer

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

monirjewel · Answer

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

mbaiseasy · Answer

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

megha_2709 · Answer

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

Bunuel · Answer

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}| .

megha_2709 · Answer

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

law258 · Answer

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  = 3sqrt(2)

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

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

E

silverprince · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In the xy plane, the vertices of a triangle have coordinates

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In the xy plane, the vertices of a triangle have coordinates

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards