find the vertex of a triangle if two of it’s vertices are (-2, 1) and(0, -3) and the centroid is at origin​

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1. Question:–

   • Find the vertex of a triangle if two its vertices are (-2,1) and (0,-3) and the centroid is at origin.

   Answer:–

   • ✬ The 3rd vertex of a triangle is (2,2)✬

   Step-by-step explanation:

   Given that:

   • Two vertices are (-2,1) and (0,-3)
   • Centroid is at origin(0,0)

   To find:

   • 3rd vertex of triangle

   Required Formula:

   • G = (x₁+x₂+x₃/3 , y₁+y₂+y₃/3)

   Then,

   ❍ Let A(x₁,y₁) = (-2,1), B(x₂,y₂) = (0,-3) , C(x₃,y₃) = (x,y) and G = (0,0) respectively.

   Applying the values,

   [tex]\\ :\implies\sf{(0,0) = \bigg( \frac{ – 2 + 0 + x}{3},\frac{1 + ( – 3) + y}{3} \bigg)} \\ \\ :\implies\sf{(0,0) = \bigg( \frac{ – 2 + x}{3},\frac{ – 2 + y}{3} \bigg)} \\ \\ :\implies \fbox{\frak{x = 2}} \: \red{ \bigstar} \: \fbox{\frak{y = 2}} \: \pink{ \bigstar} \\ \\ [/tex]

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   Verification:–

   Let us apply the value of x and y in the formula,

   [tex]\\ :\implies\sf{(0,0) = \bigg(\frac{-2+0+2}{3},\frac{1+(-3)+2}{3} \bigg)} \\ \\ :\implies\sf{(0,0) = \bigg(\frac{ – 2 + 2}{3}, \frac{ – 2 + 2}{3} \bigg)} \\ \\ :\implies\sf{(0,0) = \bigg( \frac{0}{3} ,\frac{0}{3} \bigg)} \\ \\ :\implies\sf{(0,0) = (0,0)} \\ \\ [/tex]

   • Hence,Verified.

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