Question

There exists two coordinates A (6,1) and B (4,9). C is the midpoint between A and B. Find the distance between coordinates A and C. Round your answer correct to 3 decimal places.

Answer 1

Given:

There are given that the coordinates:

`A(6,1),and,B(4,9)`

Step-by-step 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:

`C=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Where,

`x_1=6,y_1=1,x_2=4,y_2=9`

Then,

Put all the values into the above formula:

So,

`\begin{gathered} C=((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2)) \\ C=((6+4)/(2),(1+9)/(2)) \\ C=((10)/(2),(10)/(2)) \\ C=(5,5) \end{gathered}`

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:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Where,

`x_1=6,y_1=1,x_2=5,y_2=5`

Then,

Put all values into the above formula:

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ d=√((5-6)^2+(5-1)^2) \\ d=√((-1)^2+(4)^2) \end{gathered}`

Then,

`\begin{gathered} d=√((-1)^2+(4)^2) \\ d=√(1+16) \\ d=√(17) \\ d=4.123 \end{gathered}`

Final answer:

Hence, the midpoint C and distance of A and C is shown below:

`\begin{gathered} C=(5,5) \\ Distance:4.123 \end{gathered}`