If quadrilateral RSTU is a parallelogram, what are the lengths of the diagonals of the figure? (1 point) Diagonal RT is equal to and diagonal SU is equal to . Remaining Attempts : 3 R 3m+2 2n+2 S V U 8+n 4m-3 T

Answer 1

To find the lengths of the diagonals of the parallelogram RSTU (with vertices at coordinates), we need to apply the properties of a parallelogram and potentially the distance formula.

Given the points R, S, T, and U are specified by their coordinates:

• $R=(3m+2,4m-3)$
• $S=(V,8+n)$
• $T=(3m+2,4m-3)$ (assuming some coordinates here)
• $U=(8+n,2n+2)$

In a parallelogram, the diagonals bisect each other, which means their midpoints will be the same.

To find the lengths of the diagonals RT and SU, we will use the distance formula:

For diagonal RT:

• Let $R(m,n)=(3m+2,4m-3)$
• Let $T(m^{\prime },n^{\prime })=(8+n,4m-3)$

The distance $RT$ is given by the distance formula:

$$RT=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$$

For diagonal SU:

• Let $S(x_1,y_1)=(V,8+n)$
• Let $U(x_2,y_2)=(8+n,2n+2)$

Similarly, the distance $SU$ can be calculated using the same distance formula.

The outcome will depend on the particular values of $m$ and $n$ that you might be referring to.

If there are no specific coordinates available for S and U, we can substitute them with their general coordinates given.

Now, to solve:

Diagonal RT: $RT=\sqrt{(x_T-x_R{)}^2+(y_T-y_R{)}^2}$ Using the coordinates given (assuming no errors in coordinates input):

• Let’s assume the computations are based on values of $m$ and $n$.

Diagonal SU: $SU=\sqrt{(x_U-x_S{)}^2+(y_U-y_S{)}^2}$

Complete evaluating these two distance formulas to find lengths $RT$ and $SU$.

After performing algebraic simplification you should arrive at specific lengths stated with the variables $m$ and $n$.

Conclusion: For specific numerical results of diagonals $RT$ and $SU$, it is essential first to plug in the exact values for $m$ and $n$ based on your further details to get the length where you mentioned the first blank would equal to symbolically solve for $RT$ and $SU$.