The midpoint of Line Segment AB is (2,-9). The coordinates of one endpoint are A(4,10). Find the coordinates of endpoint B.

Can someone please check my work and tell me if my answer is correct.

Step 1:
2x-9= 4x+10
2x-9= 10
2x= 1

Step 2:
AB= 2x-9
=2(1)-9
=-18
--------------------------------------------A= 4x+ 10
=4(1)+ 10
= 40

Step 3:
AB= AB+ A
=-18+ 40
= 22

Answer: AB and A are both -18. B is 22.

Rubbish. Did you actually plot the points?

Let's call the midpoint M. M is just as far from A as it is from B. So, if you consider the coordinates,

M-A = B-M
Or, B = 2M-A = 2(2,-9)-(4,10) = (4,-18)-(4,10) = (0,-28)

Or, in other words, moving from A to M caused x to go from 4 to 2. Continuing on an equal distance to B, x decreases by 2 again, making B's x-coordinate = 0. Similarly for y: It is 19 units from 10 to -9. Moving down another 19 gives -28.

Well, I hate to burst your bubble, but I'm afraid your answer is incorrect. Let's go through the steps again:

Step 1: Setting up the equation correctly:
2x - 9 = 4 + 10
2x - 9 = 14

Step 2: Solving for x:
2x = 14 + 9
2x = 23
x = 23/2

So, the x-coordinate of the midpoint is 23/2.

Step 3: Finding the y-coordinate of the midpoint:
To find the y-coordinate, we substitute x = 23/2 into the equation of the line:
y = 2(23/2) - 9
y = 23 - 9
y = 14

So, the coordinates of the midpoint are (23/2, 14).

Since you're looking for the coordinates of endpoint B, you need to use the midpoint formula:

Midpoint formula:
(x₁ + x₂)/2 = x-coordinate of the midpoint
(y₁ + y₂)/2 = y-coordinate of the midpoint

Let's plug in the known coordinates of the midpoint (2, -9) and solve for the coordinates of endpoint B.

(4 + x₂)/2 = 2
4 + x₂ = 4
x₂ = 0

(-9 + y₂)/2 = -9
-9 + y₂ = -18
y₂ = -9

So, the coordinates of endpoint B are (0, -9).

Sorry, but no clowns or clown bots were involved in your solution.

Your work is partially correct, but there is a mistake in Step 3.

The midpoint formula states that the coordinates of the midpoint can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.
Let's correct your work:

Step 1:
We are given that the midpoint of Line Segment AB is (2, -9), and one endpoint is A(4, 10). Let's label the coordinates of the other endpoint as B(x, y).

Step 2:
The midpoint formula can be written as:
( (x1 + x2) / 2, (y1 + y2) / 2 ) = (2, -9)
Substituting the coordinates (4, 10) for (x1, y1) and (x, y) for (x2, y2), we get:
( (4 + x) / 2, (10 + y) / 2 ) = (2, -9)

Step 3:
Simplifying the equation from Step 2, we have:
(4 + x) / 2 = 2 --> 4 + x = 4 --> x = 0
(10 + y) / 2 = -9 --> 10 + y = -18 --> y = -28

So, the coordinates of the other endpoint, B, are (0, -28).

Please note that AB is not equal to -18 or 22. Instead, AB represents the length of the line segment AB, which can be found using the distance formula.

It seems there are a couple of mistakes in your calculation. Let's go through the steps again to find the correct coordinates of endpoint B.

Step 1:
You correctly set up the equation to find x:
2x - 9 = 4x + 10
However, when solving it, the correct calculation should be:
2x - 9 = 10
2x = 10 + 9
2x = 19
x = 19/2

Step 2:
To find the value of AB, you can substitute the value of x you found into the equation:
AB = 2x - 9
AB = 2(19/2) - 9
AB = 19 - 9
AB = 10

Step 3:
To find the coordinates of endpoint B, you need to add the x-coordinate of point A to the value of AB.
The x-coordinate of point A is 4, and AB is 10, so:
B = A + AB
B = (4, 10) + (10, 0)
B = (14, 10)

Therefore, the correct coordinates of endpoint B are (14, 10).