## Question

Two vertices of a triangle are (–1, 4) and (5, 2). If its centroid is (0, –3), find the third vertex.

### Solution

(–4, –15)

Let the third vertex be (*x*, *y*) then the coordinates of the centroid of triangle are

Hence the third vertex is (–4, –15).

**Short Cut Method :**

According to corollary 2 :

= (–4, –15).

#### SIMILAR QUESTIONS

Find the coordinates of the point which divides the line segment joining the points (5, –2) and (9, 6) in the ratio 3 : 1.

Find the length of median through *A* of a triangle whose vertices are *A*(–1, 3), B(1, – 1)and *C*(5, 1).

Determine the ratio in which *y* – *x* + 2 = 0 divides the line joining (3, –1) and (8, 9).

The coordinates of three consecutive vertices of a parallelogram are (1, 3), (–1, 2) and (2, 5). Then find the coordinates of the fourth vertex.

The mid points of the sides of a triangle are (1, 2), (0, –1) and (2, –1). Find the coordinates of the vertices of a triangle with the help of two unknowns.

Find the coordinates of a point which divides externally the line joining (1, –3) and (–3, 9) in the ratio 1: 3.

The line segment joining *A*(6, 3) to *B*(–1, –4) is doubled in length by having its length added to each end. Find the coordinates of the new ends.

Find the ratio in which the point (2, *y*) divides the line segment joining (4, 3) and (6, 3) and hence find the value of *y*.

Find the harmonic conjugates of the point *R*(5, 1) with respect to the points *P*(2, 10) and *Q*(6, –2).

The vertices of a triangle are (1, 2), (*h*, –3) and (–4, *k*). Find the value of . If the centroid of the triangle be at the point (5, –1).