Final answer:
To find the coordinates of D given midpoint M and endpoint C, use the midpoint formula. By substituting the values for M and C, and solving for D, we find that the coordinates of endpoint D are (-6, 0).
Step-by-step explanation:
To find the coordinates of the other endpoint D of the line segment CD given that the midpoint M is (-2, 1) and one endpoint C is (2, -2), we need to use the midpoint formula which relates the coordinates of the midpoint to the coordinates of the endpoints of a segment. The midpoint M of a segment with endpoints (x₁, y₁) and (x₂, y₂) is found using the equations:
M = ½(x₁ + x₂), ½(y₁ + y₂)
We can plug in our known values for M and C and solve for the unknown endpoints of D:
- Mx = ½(Cx + Dx)
- My = ½(Cy + Dy)
Substitute the given values:
- -2 = ½(2 + Dx)
- 1 = ½(-2 + Dy)
After simplifying, we find that:
- Dx = -2 * 2 - 2 = -6
- Dy = 1 * 2 - 2 = 0
The coordinates of endpoint D are (-6, 0).