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

Answer:

(-4, 2)

Step-by-step explanation:

Very nice question.

The point where the medians of a triangle intersect is the centroid.

We know that, if the coordinates of the vertices of a triangle are,

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

then the coordinates of the centroid is,

$(\frac{x_1+x_2+x_3}{2},\ \frac{y_1+y_2+y_3}{2})$

Here, the coordinates of the centroid is (1, -1).

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

Okay.

$(\frac{1+5+x}{2},\ \frac{-5+1+y}{2})=(1,\ -1) \\ \\ (\frac{x+6}{2},\ \frac{y-4}{2})=(1,\ -1)$

From x coordinates,

$\frac{x+6}{2}=1 \\ \\ x+6=1\times 2 \\ \\ x+6=2 \\ \\ x=2-6 \\ \\ x=\bold{-4}$

From y coordinates,

$\frac{y-4}{2}=-1 \\ \\ y-4=-1\times 2 \\ \\ y-4=-2 \\ \\ y=-2+4 \\ \\ y=\bold{2}$

∴ The coordinates of the third vertex is (-4, 2).

_________________________________________________

Hope this may be helpful.

Thank you. Have a nice day. :-)

#adithyasajeevan