Question

The coordinates of the centroid of triangle ABC are (1, -1). The vertices of ABC are A(-5, 3), B(p, -1), and C(6, q). What are the coordinates of vertex B?

A. B(4, -1)
B. B(1, -1)
C. B(3, -1)
D. B(0, -1)

Answer 1

To find the coordinates of vertex B in triangle ABC, we can use the centroid formula and the coordinates of the centroid. By setting up and solving an equation, we find that the coordinates of vertex B are (2, -1).

Step-by-step explanation:

To find the coordinates of vertex B, we can use the centroid formula. The centroid of a triangle is the point of intersection of its medians, and it is calculated by finding the average of the x-coordinates and the average of the y-coordinates of the three vertices.

Given that the coordinates of the centroid are (1, -1), and the coordinates of vertices A and C are (-5, 3) and (6, q) respectively, we can set up the equation:

(xA + xB + xC) / 3 = 1

Simplifying, we have:

(-5 + p + 6) / 3 = 1

Combining like terms, we get:

p + 1 = 3

solving for p, we find that p = 2. Therefore, the coordinates of vertex B are (2, -1), which corresponds to answer choice C. So, B(2, -1) is the correct answer.