find the coordinates of the missing endpoint given that S is the midpoint. Problem: T(-4,3),S(-1,5)
the length of TS must be 3 in the x, and 2 in the y. Look at how I figured that out.
So the endpoint must be (2,7) check me.
-1 = (-4 + x) divided by 2 which results in x = 2
5 = (3 + y) divided by 2 which results in y = 7
Thus the missing point is (2,7).
To find the coordinates of the missing endpoint in this problem, we need to apply the midpoint formula.
The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) can be found using the formulas:
Midpoint x-coordinate = (x₁ + x₂) / 2
Midpoint y-coordinate = (y₁ + y₂) / 2
In this problem, we are given the coordinates of point T as (-4, 3) and the midpoint S as (-1, 5).
Let's label the missing endpoint as M and its coordinates as (x, y).
Using the midpoint formula, we can set up the following equations:
Midpoint x-coordinate = (x₁ + x₂) / 2
-1 = (-4 + x) / 2
To solve for x, we multiply both sides of the equation by 2 and simplify:
-2 = -4 + x
x = -2 + 4
x = 2
Now, let's use the y-coordinate equation to find the y-coordinate of point M:
Midpoint y-coordinate = (y₁ + y₂) / 2
5 = (3 + y) / 2
To solve for y, we multiply both sides of the equation by 2 and simplify:
10 = 3 + y
y = 10 - 3
y = 7
Therefore, the missing endpoint M has coordinates (2, 7).