Question

Need help with finding the p point

Answer 1

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 $\overline{DE}$.

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.

Answer 2

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