Question

Two vertices of a triangle are (1,-5) and (5,1). The medians intersect at (1,-1). Find the third vertex of the triangle.

Answer 1

Hence, coordinates of third vertex are (-3,1).

Step-by-step explanation:

If in a ∆ABC,

$(x_1,y_1), (x_2,y_2),(x_3,y_3)$

are the coordinates of vertices of triangle.

And (x,y) be the coordinates of point where medians intersect

We know that,in a triangle where all median intersect each other is known as centroid.

Also,

$x = \frac{x_1+x_2+x_3}{3} \\ </p><p>y = \frac{y_1+y_2+y_3}{3}$

Here,

(x,y) = (1,-1)

$x =\frac{1+5+x_3}{3} \\ 1=\frac{6+x_3}{3} \\ 3=6+x_3 \\ x_3=3-6 \\ x_3=-3 \\ y=\frac{-5+1+y_3}{3} \\ -1=\frac{-4+y_3}{3} \\ -3=-4+y_3 \\ 4-3=y_3 \\ y_3=1$

Hence, coordinates of third vertex are (-3,1).