Question

The midpoint of UV is (5, -10). The coordinates of one endpoint are U(3,6). Find the coordinates of endpoint V.

Answer 1

The answer is (7, -26) for The second endpoint.  

We'll call the midpoint M. In order to find this, we must first note that to find a midpoint we need to take the average of the endpoints. To do this we add them together and then divide by 2. So, using that, we can write a formula and solve for each part of the k coordinates. We'll start with just x values.

(Ux + Vx)/2 = Mx

(Vx + 3)/2 = 5

Vx + 3 = 10

Vx = 7

And now we do the same thing for y values

(Uy + Vy)/2 = My

(Vy + 6)/2 = -10

Vy + 6 = -20

Vy = -26

This gives us the final point of (7, -26)

Answer 2

Answer:

The coordinates of point V is (7,-26)

Step-by-step explanation:

Let W be the midpoint of line UV

So, Coordinates of W = (x,y) = (5,-10)

We are given that coordinates of point U are $x_{1},y_{1}$ =(3,6)

Now to find the coordinates of point V denoted by   $x_{2},y_{2 }$ , we will use mid point formula since UV is the line and W is its midpoint .

Formula of midpoint :

$(x,y)=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2} }{2} )$

Now putting values in the formula we will get :

$(5,-10)=(\frac{3+x_{2} }{2} ,\frac{6+y_{2} }{2} )$

Thus  $x= \frac{x_{1}+x_{2} }{2}$

⇒ $5 = \frac{3+x_{2} }{2}$

⇒ $5 *2 = 3+x_{2}$

⇒ $10 = 3+x_{2}$

⇒ $10 - 3 = x_{2}$

⇒ $7 = x_{2}$

Now, $y = \frac{y_{1} +y_{2} }{2}$

⇒ $-10 = \frac{6 +y_{2} }{2}$

⇒ $-10*2 = 6 +y_{2}$

⇒ $-20 = 6 +y_{2}$

⇒ $-20 - 6 = y_{2}$

⇒ $-26 = y_{2}$

Thus,  $x_{2},y_{2 }$ =(7,-26)

Hence ,The coordinates of point V is (7,-26)