Question

In △ABC, G (− 4, − 7) is the centroid. If A

(−14, −19) and B (3, 5) then find the co-

ordinates of C.

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Answer 1

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✤ Required Answer:

✒ Provided:-

• Centroid of the triangle = (-4,-7)
• Two of the vertices of triangle = (-14,-19) and (3,5)

✒ To FinD:-

• The third vertex of the triangle?

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✤ How to solve?

Here, we have been given Centroid of the triangle which is the intersecting point of three meridians of the triangle.

• The centroid of the triangle is given by $\sf{( \frac{x_1 + x_2 + x_3}{3} ), (\frac{y_1 + y_2 + y_3}{3}})$ where (x1, y1), (x2, y2) and (x3, y3) are the vertices of the triangle.

⚘So, By using this, Let's solve the Q.

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✤ Solution:-

We have,

• Vertices of the triangle (-14,-19) and (3,5) and centroid of the triangle (-4,-7)

Assume the third vertex be (x3, y3)

$\large{ \sf{ \longrightarrow{(x \: y) = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} )}}}$

$\large{ \sf{ \longrightarrow (-4\:,-7) = ( \frac{-14 + 3 + x_3}{3} , \frac{-19 + 5 + y_3}{3} )}}$

By comparing both sides,

|| Evaluating x3 and y3 ||

➝ 3+ (-14) + x3 /3 = -4

➝ -11 + x3 = -12

➝ x3 = -12 + 11

✒ x coordinate of third vertex = -1

&

➝ -19 + 5 + y3 /3 = -7

➝ -14 + y3/ = -21

➝ y3 = -7

✒ y coordinate of third vertex = 7

☀️ So the coordinates of the third vertex of the triangle is (-1,-7) [Answer]

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Answer 2

Answer:

C is (-1, -7)

Step-by-step explanation:

A triangle ABC having centroid G. Vertices of A is (-14, -19, B is (3,5) and G is (-4,7).

Centroid is the mean position of all the points.

We have to find the coordinates of the C.

Formula used here is:

(x, y) = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3

x = (x1 + x2 + x3)/3

-4 = (-14 + 3 + x3)/3

-12 = -11 + x3

-1 = x3

Similarly,

y = (y1 + y2 + y3)/3

-7 = (-19 + 5 + y3)/3

-21 = -14 + y3

-7 = y3

Hence, the vertices of the third side of the triangle i.e. of C is (-1, -7).