I need help in this question!!!

CD has an endpoint at (2,-1) and a midpoint at (8,3). which measure is closest to the length of CD?
A. 20.4 units
B. 8.4 units
C. 14.4 units
D. 11.7 units

2√((8-2)^2+(3+1)^2) = 14.4

thank very much Steve

Why did the CD go to therapy? Because it had some serious endpoint issues and needed help finding its midpoint! Let's help it out, shall we?

To find the length of CD, we can use the distance formula. The distance formula is like a guide for measuring the length of a line segment, just like a measuring tape guides us in measuring things.

Using the distance formula, we can find the length of CD by calculating the distance between the endpoint at (2,-1) and the midpoint at (8,3).

The formula is: Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So, let's plug in the values and find the length of CD:

Distance = sqrt((8 - 2)^2 + (3 - (-1))^2)
= sqrt((6)^2 + (4)^2)
= sqrt(36 + 16)
= sqrt(52)
≈ 7.211 units (approx.)

Alright, let's check our options again:

A. 20.4 units - Whoa, that's way too big!
B. 8.4 units - A little too big, my friend.
C. 14.4 units - Nope, too large as well.
D. 11.7 units - Not even close!

None of the given options are close to 7.211 units. So, the correct answer is none of the options provided. The length of CD is approximately 7.211 units.

To find the length of CD, we can use the distance formula, which states that the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Given that the midpoint of CD is (8,3) and one endpoint is (2,-1), we can substitute these values into the formula to find the length of CD.

Let's calculate it step-by-step.

Step 1: Find the difference in x-coordinate: \(x_2 - x_1\)
\[8 - 2 = 6\]

Step 2: Find the difference in y-coordinate: \(y_2 - y_1\)
\[3 - (-1) = 4\]

Step 3: Square the difference in x-coordinate:
\[(6)^2 = 36\]

Step 4: Square the difference in y-coordinate:
\[(4)^2 = 16\]

Step 5: Add the squares of the differences:
\[36 + 16 = 52\]

Step 6: Take the square root of the sum:
\[\sqrt{52} \approx 7.21\]

The length of CD is approximately 7.21 units.

Now, comparing this with the given answer choices, we can see that the measure closest to 7.21 is:

D. 11.7 units

To find the length of CD, we can use the formula for the distance between two points on a coordinate plane. The formula is:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Given that CD has an endpoint at (2, -1) and a midpoint at (8, 3), we can substitute these values into the formula:

Distance = √((8 - 2)^2 + (3 - (-1))^2)

Simplifying further:

Distance = √(6^2 + 4^2)
Distance = √(36 + 16)
Distance = √52
Distance ≈ 7.211

Now we can compare this result with the answer choices provided:

A. 20.4 units
B. 8.4 units
C. 14.4 units
D. 11.7 units

Since the closest measure to 7.211 is 8.4 units, the answer is B. 8.4 units.