Chapter 10.3, Problem 13WE

To determine

To calculate: $y$.

Answer to Problem 13WE

  $y=3$ or $y=-1$ .

Explanation of Solution

Given information: $\overline{AU},\overline{BV}$ and $\overline{CW}$ are the medians of $\Delta ABC$ ; $BP=y^2+1$ and $PV=y+2$ .

  

Calculation:

Medians divide the midpoint in the ratio $2:1$ .

Here, $\frac{BP}{PV}=\frac{2}{1}$ ,

  $\Rightarrow BP=2PV,$

  $\Rightarrow y^2+1=2(y+2),$

  $\Rightarrow y^2-2y-3=0$ .

Therefore, $y=3$ or $y=-1$ .