A (x, 5), B (3, – 4) and C (– 6, y) are the three vertices of a triangle ABC. If (3.5, 4.5) is the centroid of the triangle, find the point (x + 3, y – 4).

Correct option is A

Given:
Coordinates of point A = (x, 5)
Coordinates of point B = (3, –4)
Coordinates of point C = (–6, y)
Centroid of triangle ABC = (3.5, 4.5)
Formula Used:
Centroid (G) of a triangle with vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃) is given by = $$\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$$​​
Solution:
Using the centroid formula:
​$$\left( \frac{x + 3 - 6}{3}, \frac{5 - 4 + y}{3} \right) = \left( 3.5, 4.5 \right)$$
​$$\left( \frac{x - 3}{3}, \frac{1 + y}{3} \right) = \left( 3.5, 4.5 \right)$$​
Equate x and y coordinates
​$$\frac{x - 3}{3} = 3.5 \Rightarrow x - 3 = 10.5 \Rightarrow x = 13.5\\\frac{1 + y}{3} = 4.5 \Rightarrow 1 + y = 13.5 \Rightarrow y = 12.5$$​​
Now, find (x + 3, y – 4):
(13.5 + 3, 12.5 – 4) = (16.5, 8.5)