Final answer:
The mathematical problem concerns finding the unknown endpoint of a line segment with given endpoint C(-2,6) and midpoint M(1,1). By applying the midpoint formula, it is determined that the coordinates for the other endpoint D are (4, -4).
Step-by-step explanation:
To find the other endpoint of line CD, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the coordinates of its endpoints. In this case, we know that the midpoint of line CD is (1,1) and one endpoint is C(-2,6). Let's denote the other endpoint as D(x,y).
We can use the midpoint formula to solve for the values of x and y:
(-2 + x) / 2 = 1 (x-coordinate)
(6 + y) / 2 = 1 (y-coordinate)
Simplifying these equations gives:
-2 + x = 2 => x = 4
6 + y = 2 => y = -4
Therefore, the other endpoint of line CD is D(4,-4).
The subject of this question is Mathematics, and it pertains to finding the other endpoint of a line segment when one endpoint and the midpoint are known. In this case, we're given endpoint C(-2, 6) and midpoint MCD(1, 1) of line CD, and we need to find the coordinates of the other endpoint D.
To find the coordinates of endpoint D, we use the midpoint formula:
Midpoint M(x,y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Here, (x1, y1) is the coordinate of endpoint C and (x2, y2) is the coordinate of endpoint D that we are looking for. We substitute the known values and solve for x2 and y2 which are the coordinates of endpoint D:
1 = (-2 + x2) / 2
1 = (6 + y2) / 2
Solving these equations, we find:
x2 = 2 * 1 + 2 = 4
y2 = 2 * 1 - 6 = -4
Therefore, the coordinates of endpoint D are (4, -4).