Question

You need to consider the points (1,-5) and ( 2, 12). You need also state the midpoint of the line segment with the given endpoints.

Answer 1

step 1

Find out the midpoint

we have the points

(1,-5) and (2,12)

The formula to calculate the midpoint between two points is equal to

`C((x1+x2)/(2),(y1+y2)/(2))`

substitute the given values

`C((1+2)/(2),(-5+12)/(2))`
`C((3)/(2),(7)/(2))`

so the midpoint is C(1.5,3.5)

step 2

we have that

the center of the circle is the midpoint C(1.5,3.5)

Find out the radius

Remember that

the distance between the center and any point that lies on the circle is equal to the radius

we have the points

C(1.5,3.5) and (2,12)

Find out the distance (radius)

`d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}`

substitute given values

`d=\sqrt[]{(12-3.5)^2+(2-1.5)^2}`
`d=r=\sqrt[]{(8.5)^2+(0.5)^2}`
`\begin{gathered} r=\sqrt[]{72.5} \\ r=\sqrt[]{(145)/(2)} \end{gathered}`

the equation of the circle is equal to

`(x-(3)/(2))^2+(y-(7)/(2))^2=(\sqrt[]{(145)/(2)})^2`

simplify

`(x-(3)/(2))^2+(y-(7)/(2))^2=(145)/(2)`