I think my teacher might have made a mistake while grading homework. I'd like a second opinion if possible..
Q; The midpoint of line UV is (5,-11). The coordinate of one endpoint are U (3,5). Find the coordinates of the endpoint V.
My answer was V(7,-27)
If I'm wrong can you explain to me why.. sorry I know I'm asking a lot.
my solution:
let the other end point be (x,y)
to get the x:
(x+3)/2 = 5
x+3 = 10
x = 7
to get the y:
(y+5)/2 = -11
x+5 = -22
y = -27
You had that, good job
I agree, your teacher is in error.
Thank you, I'll have to get in contact with my teacher
To find the coordinates of the endpoint V, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment (x₁, y₁) and (x₂, y₂) can be found using the following formulas:
Midpoint x-coordinate: (x₁ + x₂) / 2
Midpoint y-coordinate: (y₁ + y₂) / 2
In this case, you were given that the midpoint of line UV is (5, -11) and one endpoint is U(3, 5).
So, let's substitute the values into the formula:
Midpoint x-coordinate: (3 + x₂) / 2 = 5
Midpoint y-coordinate: (5 + y₂) / 2 = -11
Simplifying the equations:
(3 + x₂) / 2 = 5
3 + x₂ = 5 * 2
3 + x₂ = 10
x₂ = 10 - 3
x₂ = 7
(5 + y₂) / 2 = -11
5 + y₂ = -11 * 2
5 + y₂ = -22
y₂ = -22 - 5
y₂ = -27
So, according to the given information and calculations, the coordinates of endpoint V are V(7, -27). Your answer is correct!