Question

Let C be the centroid of the triangle with vertices (3, –1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y – 1 = 0 and 3x – y + 1 = 0. Then the line passing through the points C and P also passes through the point ______.

Options

• (–9, –6)

• (9, 7)

• (7,6)

• (–9, –7)

Answer 1

Let C be the centroid of the triangle with vertices (3, –1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y – 1 = 0 and 3x – y + 1 = 0. Then the line passing through the points C and P also passes through the point (9, 7).

Explanation:

Coordinates of centroides

C = `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`

= `((3 + 1 + 2)/3, (-1 + 3 + 4)/3)`

= (2, 2)

The given equation of lines are

x + 3y – 1 = 0  ...(i)

3x – y + 1 = 0  ...(ii)

Then, from (i) and (ii)

Point of intersection P`(-1/5, 2/5)`

Equation of line DP

8x – 11y + 6 = 0