Point p is the midpoint of DE. DP =3x + 2 and DE = 10x - 12. What is the length of DP
2 answers:
<h2>
Answer:</h2>
The length of DP is:
DP=14 units
<h2>
Step-by-step explanation:</h2>
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
If P <span>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</span>
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