Question

Point p is the midpoint of DE. DP =3x + 2 and DE = 10x - 12. What is the length of DP

Answer 1

Answer:

The length of DP is:

                      DP=14 units

Step-by-step explanation:

It is given that:

Point P is the midpoint of DE.

DP =3x + 2 and DE = 10x - 12.

We know that a midpoint divides the given line segment into two equal parts (i.e. it bisects a line segment)

Hence, we have:

DP+PE=DE

Also, DP=PE

This means that:

2DP=DE

2(3x+2)=10x-12

2×(3x)+2×2=10x-12

6x+4=10x-12

10x-6x=4+12

4x=16

x=16/4

x=4

Hence,

DP=3x+2=3×4+2

i.e.

DP=14

Answer 2

If P is the midpoint of DE then 
DE = 2(DP)
10x - 12 = 2(3x + 2)
10x - 12 = 6x + 4
10x - 6x = 4 + 12
4x = 16
x = 16/4
x = 4

DP = 3x + 2 = 3 * 4 + 2 = 12 + 2 = 14 units