Respuesta :
Given:
There are given that the coordinates:
[tex]A(6,1),and,B(4,9)[/tex]Explanation:
First, we need to find the mid-point of c by using the given coordinate point A and B.
Then,
To find the midpoint, we need to use the midpoint:
So,
Fro the formula of midpoint:
[tex]C=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where,
[tex]x_1=6,y_1=1,x_2=4,y_2=9[/tex]Then,
Put all the values into the above formula:
So,
[tex]\begin{gathered} C=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}) \\ C=(\frac{6+4}{2},\frac{1+9}{2}) \\ C=(\frac{10}{2},\frac{10}{2}) \\ C=(5,5) \end{gathered}[/tex]So,
The point of C is, (5, 5).
Now,
We need to find the distance between A(6,1)and C(5,5):
So,
From the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where,
[tex]x_1=6,y_1=1,x_2=5,y_2=5[/tex]Then,
Put all values into the above formula:
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(5-6)^2+(5-1)^2} \\ d=\sqrt{(-1)^2+(4)^2} \end{gathered}[/tex]Then,
[tex]\begin{gathered} d=\sqrt{(-1)^2+(4)^2} \\ d=\sqrt{1+16} \\ d=\sqrt{17} \\ d=4.123 \end{gathered}[/tex]Final answer:
Hence, the midpoint C and distance of A and C is shown below:
[tex]\begin{gathered} C=(5,5) \\ Distance:4.123 \end{gathered}[/tex]