Question

5. Determine the value of each variable for parallelogram INDY that has diagonals that intersect at P.IP = 3x, DP = 6x-2, NP = 3y, and YP = 7x - 2.

Answer 1

Given the INDY

The diagonals has intersected at the point P

IP = 3x, DP = 6x - 2

NP = 3y , YP = 7x - 2

So, IP = DP

`6x-2=3x`

Solve for x :

`\begin{gathered} 6x-2=3x \\ 6x-3x=2 \\ 3x=2 \\ \\ x=(2)/(3) \end{gathered}`

And : NP = YP

`3y=7x-2`

substitute with the value of x :

`\begin{gathered} 3y=7\cdot(2)/(3)-2=(23)/(3)-2=(17)/(3) \\ \\ y=(17)/(9) \end{gathered}`

So, the answer is :

`\begin{gathered} x=(2)/(3) \\ \\ y=(17)/(9) \end{gathered}`