In the xy-plane, what is the perimeter of the triangle with vertices a

Question

In the 𝑥𝑦-plane, what is the perimeter of the triangle with vertices at (0, 0), (3, 4), and (−1, 7)?

(A) 25 
(B)  4 \sqrt{5} 
(C)  10 + 5 \sqrt{2} 
(D)  10 + 3 \sqrt{7} 
(E)  5 + 10 \sqrt{2}

gmatophobia · Answer

We can find the distance, d, between  (x_1,y_1)  and  (x_2,y_2)  using the equation

d = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}

This will help get the distance between each of the points, thereby get the length of each side of the triangle.

Once the length is obtained, the same can be added to get the perimeter.

Option C

SaquibHGMATWhiz · Answer

Solution:

We are asked about the perimeter of the triangle with vertices A(0, 0), B(3, 4), and C(−1, 7) 
 Length of  AB=\sqrt{(3-0)^2+(4-0)^2}=\sqrt{9+16}=\sqrt{25}=5  
 Length of  BC=\sqrt{(-1-3)^2+(7-4)^2}=\sqrt{16+9}=\sqrt{25}=5  
 Length of  CA=\sqrt{(-1-0)^2+(7-0)^2}=\sqrt{1+49}=\sqrt{50}  
 Perimeter  =AB+BC+CA=5+5+\sqrt{50}=10+\sqrt{50}=10+5\sqrt{2}

Hence the right answer is    Option C

In the xy-plane, what is the perimeter of the triangle with vertices a

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In the xy-plane, what is the perimeter of the triangle with vertices a

Prep Toolkit

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

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My Rewards