Answer :
Answer:
(1,-4)
Step-by-step explanation:
Midpoint Formula
The midpoint formula finds the point that's in the middle between two given points. The distance between the two points are the same.
[tex]\left(\dfrac{x_1+x_2}{2} ,\dfrac{y_1+y_2}{2} \right) = (x_m,y_m)[/tex]
[tex]\dotfill[/tex]
Diameter
Diameter is the length from one end of the circle, through its center to the opposite end (collinear to the initial point).
The diameter is twice the length of the circle's radius, meaning that the distance from each end to the center is the radius' length.
[tex]\hrulefill[/tex]
Solving the Problem
We're given
- the circle's center: (2,1)
- one of the circle's endpoints: (3,6)
and we're told to find the coordinates of the other endpoint.
Since the distance between each endpoint and the circle's center are the same, we can consider the center to be the midpoint of the two endpoints. We can plug in all the known values and solve for the missing ones.
[tex]\left(\dfrac{3+x_2}{2} ,\dfrac{6+y_2}{2} \right) = (2,1)[/tex]
We can break this down into two sets of equations:
[tex]\dfrac{3+x_2}{2}=2[/tex]
[tex]\dfrac{6+y_2}{2}=1[/tex].
Solving for the x-value of the coordinate.
[tex]3+x_2=4[/tex]
[tex]x_2=1[/tex]
Solving for the y-value of the coordinate.
[tex]6+y_2=2[/tex]
[tex]y_2=-4[/tex]
So, the other endpoint is (1,-4).
Answer:
(1, - 4 )
Step-by-step explanation:
Using the midpoint formula
• M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
where (x₁, y₁ ) , (x₂, y₂ ) are the endpoints of a segment and M is the midpoint.
The centre of a circle is at the midpoint of the diameter
Given one endpoint is (3, 6 ) and M = (2, 1 )
let the other endpoint have coordinates (x, y )
Using the midpoint formula , equate the x and y coordinates to M
[tex]\frac{x+3}{2}[/tex] = 2 ( multiply both sides by 3 )
x + 3 = 4 ( subtract 3 from both sides )
x = 1
and
[tex]\frac{y+6}{2}[/tex] = 1 ( multiply both sides by 2 )
y + 6 = 2 ( subtract 6 from both sides )
y = - 4
The coordinates of the other endpoint of the diameter is (1, - 4 )
