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If P is a midpoint of DE, then:

DP + PE = DE and DP = PE → 2DP = DE

We have:

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

Substitute:

2(3x + 2) = 10x - 12     |use distributive property

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

6x + 4 = 10x - 12     |subtract 4 from both sides

6x = 10x - 16     |subtract 10x from both sides

-4x = -16    |divide both sides by (-4)

x = 4

Substitute the value of x to the equation DP = 3x + 2:

|DP = 3(4) + 2 = 12 + 2 = 14

Answer: DP = 14 units

Answer:

Length of DP is, 14 units

Step-by-step explanation:

Midpoint: a point that divides the line segment into two equal parts.

Given: P is the midpoint of [tex]\overline{DE}[/tex].

Also, [tex]DP = 3x+2[/tex] and [tex]DE = 10x-12[/tex]

To find the length of [tex]\overline{DP}[/tex].

Since P is the midpoint [tex]\overline{DE}[/tex] then, we have from the definition [tex]DP=PE[/tex].

Since, [tex]DE=DP+PE[/tex]=[tex]DE=DP+DP=2DP[/tex]

then, we have [tex]10x-12=2(3x+2)[/tex]

Use distributive property on left hand side: [tex]a(b+c)=a\cdot b+a\cdot c[/tex]

∴[tex]10x-12=6x+4[/tex]

[tex]10x-6x=12+4[/tex]

[tex]4x=16[/tex]

On simplifying we get,

[tex]x=4[/tex]

Now, put the value of x=4 in  DP=3x+2;

⇒ [tex]DP=3\cdot4+2=12+2=14[/tex]

therefore, the length of DP is 14 units.

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