Question

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

Answer 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,

$\\ :\implies\sf{(0,0) = \bigg( \frac{ - 2 + 0 + x}{3},\frac{1 + ( - 3) + y}{3} \bigg)} \\ \\ :\implies\sf{(0,0) = \bigg( \frac{ - 2 + x}{3},\frac{ - 2 + y}{3} \bigg)} \\ \\ :\implies \fbox{\frak{x = 2}} \: \red{ \bigstar} \: \fbox{\frak{y = 2}} \: \pink{ \bigstar}$

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Verification:-

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

$\\ :\implies\sf{(0,0) = \bigg(\frac{-2+0+2}{3},\frac{1+(-3)+2}{3} \bigg)} \\ \\ :\implies\sf{(0,0) = \bigg(\frac{ - 2 + 2}{3}, \frac{ - 2 + 2}{3} \bigg)} \\ \\ :\implies\sf{(0,0) = \bigg( \frac{0}{3} ,\frac{0}{3} \bigg)} \\ \\ :\implies\sf{(0,0) = (0,0)}$

• Hence,Verified.

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