A line segment XY has an endpoint and the midpoint is ..? (3,0) - X (8,5)- M. What are the coordinates of the endpoint Y?
Looks to me more like (3,0) - X (8,5)- M means
X = (3,0) and M = (8,5)
That makes Y = (13,10)
no idea what (3,0) - X (8,5)- M.
is supposed to say
I will assume one end point is X(8,5) and the midpoint is M(3,0)
let the other endpoint be Y(a,b)
for the x's :
(a+8)/2 = 3
a+8 = 6
x = -2
for the y's
(b+5)/2 = 0
b+5=0
b= -5
the other endpoint is Y(-2, -5)
If that is not what you meant, make the necessary changes, by
following my method. The method is correct
To find the coordinates of endpoint Y, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint, (x, y), is the average of the x-coordinates and the average of the y-coordinates of the two endpoints.
Let's call the coordinates of endpoint Y (x₂, y₂). We are given the coordinates of endpoint X as (3, 0) and the coordinates of the midpoint M as (8, 5).
The midpoint formula is:
x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2
Substituting the given values into the formula, we have:
8 = (3 + x₂) / 2
5 = (0 + y₂) / 2
Simplifying each equation, we get:
16 = 3 + x₂
10 = y₂
Now, solve for x₂ and y₂:
16 - 3 = x₂
13 = x₂
Therefore, the coordinates of endpoint Y are (13, 10).