Question

N is the centroid Find AN account if AN =x+4 and NU=2x-1 Over 2

Answer 1

The centroid of a triangle is the point of interection of all the three medians and they have the following property:

`(AN)/(NU)=(BN)/(NV)=(2)/(1)`

Then, we have the following result:

`(AN)/(NU)=2`

By substituting the given information into this equation, we have

`(x+4)/((2x-1)/(2))=2`

or equivalently,

`(2(x+4))/(2x-1)=2`

Now, by multiplying both sides by 2x-1, we get

`2(x+4)=2(2x-1)`

and by dividing both sides by 2, we obtain

`x+4=2x-1`

We can obtain this last result if we distribute the number 2 into the parenthesis and divide the result by 2, that is,

`\begin{gathered} \text{distributing the number 2: 2x+8=4x-2} \\ \text{dividing both sides by 2: x+4=2x-1} \end{gathered}`

Now, by subtracting x to both sides of the last resutl, we have

`4=x-1`

and by adding 1 to both sides, we obtain

`5=x`

or equivalently, x=5.

Finally, in order to obtain AN, we must substitute the last result into the expression for AN. It yields,

`AN=x+4\Rightarrow AN=5+4`

Therefore, the answer is: AN = 9