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:
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 [tex]x_{1},y_{1}[/tex] =(3,6)
Now to find the coordinates of point V denoted by [tex]x_{2},y_{2 }[/tex] , we will use mid point formula since UV is the line and W is its midpoint .
Formula of midpoint :
[tex](x,y)=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2} }{2} )[/tex]
Now putting values in the formula we will get :
[tex](5,-10)=(\frac{3+x_{2} }{2} ,\frac{6+y_{2} }{2} )[/tex]
Thus [tex] x= \frac{x_{1}+x_{2} }{2}[/tex]
⇒ [tex] 5 = \frac{3+x_{2} }{2}[/tex]
⇒ [tex] 5 *2 = 3+x_{2}[/tex]
⇒ [tex] 10 = 3+x_{2}[/tex]
⇒ [tex] 10 - 3 = x_{2}[/tex]
⇒ [tex] 7 = x_{2}[/tex]
Now, [tex] y = \frac{y_{1} +y_{2} }{2}[/tex]
⇒ [tex] -10 = \frac{6 +y_{2} }{2}[/tex]
⇒ [tex] -10*2 = 6 +y_{2}[/tex]
⇒ [tex] -20 = 6 +y_{2}[/tex]
⇒ [tex] -20 - 6 = y_{2}[/tex]
⇒ [tex] -26 = y_{2}[/tex]
Thus, [tex]x_{2},y_{2 }[/tex] =(7,-26)
Hence ,The coordinates of point V is (7,-26)
