Question

The midpoint of is m(–1, –2). one endpoint is c(–9, –4). find the coordinates of the other endpoint d. a) (-11, -8)

b) (-5, -8)
c) (7, 0)
d) (7, -1)

Answer 1

The coordinates of the other endpoint D, given the midpoint M(-1, -2) and one endpoint C(-9, -4), are (7, -4) after solving the equations derived from the midpoint formula.

Step-by-step explanation:

To find the other endpoint D of a line segment when you are given the midpoint M and one endpoint C, you can use the midpoint formula which states that the coordinates of the midpoint are the averages of the coordinates of the endpoints. Here, we have M(-1, -2) and C(-9, -4), and we want to find D(x, y).

The midpoint M's coordinates are the averages of the corresponding coordinates of C and D. This gives us two equations:

1. The average of the x-coordinates: (-9 + x) / 2 = -1
2. The average of the y-coordinates: (-4 + y) / 2 = -2

Now, we can solve for x and y to find the coordinates of D.
Solving the first equation for x:
-9 + x = -2 * 2
x = -4 + 9
x = 5

Solving the second equation for y:
-4 + y = -4 * 2
y = -8 + 4
y = -4

Therefore, the coordinates of the other endpoint D are (7, -4).