Question

Find the coordinates of third vertex of a triangle, if centroid of the triangle is (3,- 5) and two of its vertices are (4, -8) and (3, 6).​

Answer 1

Answer:

Let the coordinates of the third vertex be (x, y). Then,

3x+3−7 =2and 3

y−5+4 =−1⇒x−4=6andy−1=−3⇒x=10andy=−2

Thus,the coordinates of the third vertex are (10, -2)

Answer 2

Given: Centroid of a triangle is (3, -5) and two of its vertices are (4, -8) and (3, 6).​

To find: The coordinates of the third vertex of the triangle.

Solution:

• Let the two given vertices be A (x₁, y₁) and B (x₂, y₂) and the centroid be D (x, y).
• Let the third vertex be C (x₃, y₃).
• The formula to find the centroid of a triangle is given as,

        $(x, y) = ( \frac{x_{1}+x_{2}+x_{3}}{3} , \frac{y_{1}+y_{2}+y_{3}}{3} )$

• On replacing the terms with the values given in the question, the obtained equation is,

        $(3, -5) = ( \frac {4 + 3 + x_{3}}{3} , \frac{-8 + 6 +y_{3}}{3} )$

• Now, the x and y components are separated and then, the third vertex C (x₃, y₃) can be calculated.

        $3 = \frac{4 + 3 + x_{3}}{3}$

        $x_{3} = 2$

        $-5 = \frac{-8 + 6 + y_{3}}{3}$

        $y_{3} = -13$

Therefore, the coordinates of the third vertex of the triangle are 2 and -13. Hence, C = (2, -13)