The midpoint of UV is (5,-11). The coordinates of one endpoint are U(3,5). Find the coordinates of endpoint V.

(please show work and explain.)

If we call the midpoint M, then the coordinates of M are halfway from U to V.

M = (5,-11) = (3,5)+(2,-16)
V = (5,-11) + (2,-16) = (7,-27)

ddm: They got 2, -16 because they did -11 - 5 which is -16 and 5 - 3 =2. If that makes sense.

how did you get (2,-16)?

Well, isn't it quite convenient that the midpoint of UV is given as (5, -11)? It's like a gift from the mathematical gods!

Anyway, to find the coordinates of endpoint V, let's use a little mathematical trickery.

The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the coordinates of its endpoints. So, we can set up the following equation:

[(x₁ + x₂) / 2, (y₁ + y₂) / 2] = (5, -11)

Plugging in the coordinates of U, we have:

[(3 + x₂) / 2, (5 + y₂) / 2] = (5, -11)

Now, let's solve for x₂ and y₂ separately.

For the x-coordinate:
(3 + x₂) / 2 = 5

Multiply both sides by 2:
3 + x₂ = 10

Subtract 3 from both sides:
x₂ = 7

For the y-coordinate:
(5 + y₂) / 2 = -11

Multiply both sides by 2:
5 + y₂ = -22

Subtract 5 from both sides:
y₂ = -27

So, the coordinates of endpoint V are V(7, -27).

Ta-da! We've found V, thanks to the midpoint formula and a little bit of humorous mathematical magic.

To find the coordinates of endpoint V, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) between two points (A and B) can be found by averaging the corresponding coordinates of A and B.

The midpoint formula is given as:

M = [(x1 + x2)/2, (y1 + y2)/2]

Given that the midpoint of UV is (5, -11), which is equivalent to M(5, -11), and one endpoint U is (3, 5), which is equivalent to A(3, 5), we can substitute these values into the midpoint formula:

5 = (3 + x2)/2 (Equation 1)
-11 = (5 + y2)/2 (Equation 2)

We need to isolate x and y in each equation to find the coordinates of endpoint V.

Equation 1:
Multiply both sides by 2:
10 = 3 + x2
Subtract 3 from both sides:
x2 = 7

Equation 2:
Multiply both sides by 2:
-22 = 5 + y2
Subtract 5 from both sides:
y2 = -27

Therefore, the coordinates of endpoint V are (7, -27).

In summary, to find the coordinates of endpoint V, we used the midpoint formula and substituted the values of the midpoint and one endpoint. We then solved the resulting equations to find the x-coordinate (7) and y-coordinate (-27) of endpoint V.