Question

Use the diagram and figure out if it is a diagram

Answer 1

a)

The figure PQRS is a parallelogram, this means that

QR||PS

QP||RS

And the diagonals PR and QS bisect each other in the midpoint, this means that the cut each other in equal segments so that:

PT=TR

QT=TS

Given

PT=2x and TR=x+2 we can determine the equation

`\begin{gathered} PT=TR \\ 2x=x+2 \end{gathered}`

From this equation we can determine the value of x, you have to pass the "x" term from the right side to the left side by applying the inverse operation to both sides of the equal sign:

`\begin{gathered} 2x-x=x-x+2 \\ x=2 \end{gathered}`

QT=y+12 and TS=7y we can determine the equation

`y+12=7y`

From this expression you can determine the value of y, first pass the y term to the right side of the equation by performing the inverse operation to both sides

`\begin{gathered} y-y+12=7y-y \\ 12=6y \end{gathered}`

Next divide both sides of the equation by 6 to reach the value of y

`\begin{gathered} (12)/(6)=(6y)/(6) \\ y=2 \end{gathered}`

So x=2 and y=2