Question

Point D is the centroid of triangle ABC. Given CD=x+1 and GC=x+6, find x.

Answer 1

To find x when D is the centroid of triangle ABC, apply the Centroid Theorem that states the medians are divided in a 2:1 ratio by the centroid. Using the given lengths CD=x+1 and GC=x+6, set up and solve the equation 2x+12=x+1 leading to a result of x=-11.

Step-by-step explanation:

The question relates to finding the value of x when point D is the centroid of triangle ABC and has given segments CD and GC with their lengths in terms of x.

The key property to use here is that in a centroid divides medians in a 2:1 ratio, with the portion between the vertex and the centroid being twice as long as the portion between the centroid and the midpoint of the opposite side. This is known as the Centroid Theorem.

Mathematically, we can set up the following equation based on the given information:

• 2(GC) = CD

By substituting the given lengths:

• 2(x + 6) = x + 1

Now, we can find x by solving the equation:

1. 2x + 12 = x + 1
2. x = -11

Therefore, the value of x is -11.