Question

Point D is the centroid of ∆ABC, DC = 8x - 6, and ED = 3x + 2. What is CE?​

Answer 1

See below.

Explanation:

For this problem, we are asked to solve for CE.

Because Point D is a Centroid, CE is a median.

What is a Median?

A Median is a line that connects from 1 vertex of a Triangle, through the Centroid, and then ending on the midpoint of the opposite side.

The distance from the Triangles' Vertex to the Centroid is 2 times the distance from the Centroid to the Midpoint.

Basically;

`ED = (1)/(2) CD`

Let's solve for x first.

`3x+2=(1)/(2) (8x-6)`

Distribute:

`3x+2=4x-3`

Subtract 4x from both sides:

`-x+2=-3`

Subtract 2 from both sides:

`-x=-5`

Divide by -1:

`x=5.`

CD, and DE are 2 parts of CE. When we add CD, and DE together we will have the value of CE.

`CD+DE=CE.`

Let's identify CD and DE first since we have the value of x.

`CD=8(5)-6=34.`

`DE=3(5)+2=17.`

Add:

`34+17=51 \ (CE)`

Our final answer is D, CE = 51.