Question

Point P is the midpoint of DEDP=6x +4, and DE = 141 - 10What is the length of DP?Enter your answer in the box.units

Answer 1

The given problem can be exemplified in the following diagram:

Since we are told that "P" is a mid-point of DE, this means that:

$DP=PE$

Also, since DE represents the entire segment, this means:

$DP+PE=DE$

Therefore, we may replace the values of DP and PE as "6x + 4" and we also replace the given values of DE, we get:

$(6x+4)+(6x+4)=14x-10$

Adding like terms we get:

$12x+8=14x-10$

Now we solve for "x" first by subtracting 14x from both sides:

$\begin{gathered} 12x-14x+8=14x-14x-10 \\ -2x+8=-10 \end{gathered}$

Now we subtract 8 from both sides:

$\begin{gathered} -2x+8-8=-10-8 \\ -2x=-18 \end{gathered}$

Now we divide both sides by -2:

$x=-\frac{18}{-2}=9$

Therefore, the value of "x" is 9. Now we determine the length of DP using the expression for this segment:

$DP=6x+4$

Replacing the value of "x":

$DP=6(9)+4$

Solving the operations we get:

$DP=58$

Therefore, the length of DP is 58 units.