Final answer:
To find the coordinates of endpoint T, given midpoint M and endpoint S, you use the midpoint formula to set up a system of equations. Solving for x2 and y2 gives you the coordinates of T, which are found to be (-1, -1). Therefore, the correct answer is option a) T (-1, -1).
Step-by-step explanation:
A student has asked for assistance in finding the coordinates of the other endpoint T for line segment ST, given that the midpoint M=(-3, 2) and one endpoint S= (-5,5). To solve this, we use the midpoint formula which states that the midpoint coordinates are the averages of the coordinates of the endpoints.
The midpoint formula is given as:
M = ((x1 + x2)/2, (y1 + y2)/2)
Where (x1, y1) and (x2, y2) are the coordinates of endpoints S and T, respectively, and M is the midpoint.
We already know that:
- M = (-3, 2)
- S = (-5, 5) (x1, y1)
Let's denote T as (x2, y2). We can set up the following system of equations based on the midpoint:
(-5 + x2)/2 = -3
(5 + y2)/2 = 2
By solving each equation, we find:
x2 = -1 and
y2 = -1
Thus, the coordinates of T are T (-1, -1).