23.1k views
2 votes
Segment CD has a midpoint at point M. CM is 10(x-3) units long and MD is 2(3x-5) units long. What is the length of segment CD?

User Jewelsea
by
7.8k points

1 Answer

5 votes

Answer: 12x - 20 units

Explanation:

To find the length of segment CD, you can use the formula for the distance between two points, which is given by the midpoint formula:

Midpoint formula: M = (1/2)(C + D)

In this case, C and D are the endpoints of segment CD, and M is the midpoint. The formula for the distance between C and D is:

CD = 2 * MD

Now, let's use the given information:

CM = 10(x - 3) units

MD = 2(3x - 5) units

First, find the coordinates of M using the midpoint formula:

M = (1/2)(C + D)

Since M is the midpoint, it is also the average of C and D:

M = (C + D)/2

Now, plug in the expressions for CM and MD:

M = [(10(x - 3), 2(3x - 5))/2

Simplify the expression inside the brackets:

M = (5(x - 3), 3x - 5)

Now, let's find the coordinates of C and D:

C = (10(x - 3), 0)

D = (0, 2(3x - 5))

Now, apply the midpoint formula to find M:

M = [(C + D)/2]

M = [(10(x - 3), 0 + 0, 2(3x - 5))/2]

Now, simplify further:

M = [(10(x - 3), 2(3x - 5))/2]

Now, we have the coordinates of M, which are (5(x - 3), 3x - 5).

To find CD, use the distance formula:

CD = 2 * MD

CD = 2 * [2(3x - 5)]

CD = 4(3x - 5)

Now, simplify:

CD = 12x - 20

So, the length of segment CD is 12x - 20 units.

User Ron Kalian
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories