Question

Need help with finding the p point

Answer 1

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 2

Length of DP is, 14 units

Explanation:

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

Given: P is the midpoint of
`\overline{DE}`.

Also,
`DP = 3x+2` and
`DE = 10x-12`

To find the length of
`\overline{DP}`.

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

Since,
`DE=DP+PE`=
`DE=DP+DP=2DP`

then, we have
`10x-12=2(3x+2)`

Use distributive property on left hand side:
`a(b+c)=a\cdot b+a\cdot c`

∴
`10x-12=6x+4`

`10x-6x=12+4`

`4x=16`

On simplifying we get,

`x=4`

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

⇒
`DP=3\cdot4+2=12+2=14`

therefore, the length of DP is 14 units.