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Given the three points below, what is the area of the triangle formed

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Given the three points below, what is the area of the triangle formed  [#permalink]

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New post 16 Apr 2017, 05:00
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Given the three points below, what is the area of the triangle formed by connecting them?

(0,3), (-3,-3), (3,-3)

(A) 4.5
(B) 9
(C) 18
(D) 36
(E) 72

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Re: Given the three points below, what is the area of the triangle formed  [#permalink]

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New post 16 Apr 2017, 10:50
With the given co-ordinates find the distance between the two points using \(\sqrt{(x2-x1)^2 + (y2-y1)^2}\)
Distance between points (0,3) & (3,-3) is \(\sqrt{-3^2+-6^2}\)=\(\sqrt{45}\)
Distance between points (0,3) & (-3,-3) is \(\sqrt{3^2+-6^2}\) = \(\sqrt{45}\)
Distance between points (-3,-3) & (3,-3) is\(\sqrt{-6^2 +0}\)= 6

which is an isosceles triangle.
We need to find the height so that we can use the formula \(\frac{1}{2}\)*b*h
Height by Pythagoras theorem, h=\(\sqrt{45-6}\)= \(\sqrt{36}\)= 6

Area =\(\frac{1}{2}\)*6*6
=18
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Given the three points below, what is the area of the triangle formed  [#permalink]

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New post 16 Apr 2017, 11:34
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saswata4s wrote:
Given the three points below, what is the area of the triangle formed by connecting them?

(0,3), (-3,-3), (3,-3)

(A) 4.5
(B) 9
(C) 18
(D) 36
(E) 72


(Ax,Ay)=(0,3)
(Bx,By)=(-3,-3)
(Cx,Cy)=(3,-3)

Area of a triangle = [Ax(By-Cy)+Bx(Cy-Ay)+Cx(Ay-By)]/2
= [0-3*(-3-3)+3*(3+3)]/2
=(18+18)/2 = 18


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Given the three points below, what is the area of the triangle formed  [#permalink]

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New post 16 Apr 2017, 13:30
saswata4s wrote:
Given the three points below, what is the area of the triangle formed by connecting them?

(0,3), (-3,-3), (3,-3)

(A) 4.5
(B) 9
(C) 18
(D) 36
(E) 72


base=6 [3-(-3)]
height=6 [3-(-3)]
area=1/2*6*6=18
C
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Given the three points below, what is the area of the triangle formed  [#permalink]

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New post 15 Nov 2017, 12:45
1
Top Contributor
saswata4s wrote:
Given the three points below, what is the area of the triangle formed by connecting them?

(0,3), (-3,-3), (3,-3)

(A) 4.5
(B) 9
(C) 18
(D) 36
(E) 72


Here's a sketch of the triangle:
Image

From here, we can see that the base has length 6, and the height is 6
Image

Area = (base)(height)/2
= (6)(6)/2
= 36/2
= 18
= C

Cheers,.
Brent
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Given the three points below, what is the area of the triangle formed &nbs [#permalink] 15 Nov 2017, 12:45
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