Question

for a line segment DE, one endpoint is D^(6),5 and the midpoint is M 4,2. Find the coordinates of endpoint E

Answer 1

To find the coordinates of endpoint E, use the midpoint formula with the given coordinates of D(6,5) and M(4,2). After setting up equations based on the formula, solve to find that E has coordinates of (2, -1).

Step-by-step explanation:

To find the coordinates of endpoint E of the line segment DE when given one endpoint D(6,5) and the midpoint M(4,2), we can use the midpoint formula which states that the midpoint is the average of the x-coordinates and the y-coordinates of the endpoints. Thus, if M is the midpoint between D and E, we have:

M(x) = (D(x) + E(x)) / 2 and M(y) = (D(y) + E(y)) / 2.

By plugging in the given values and solving for E(x) and E(y), we find:

4 = (6 + E(x)) / 2 and 2 = (5 + E(y)) / 2.

Which gives us the equations:

• 8 = 6 + E(x)
• 4 = 5 + E(y)

By solving these equations, we find the coordinates of E:

• E(x) = 8 - 6 = 2
• E(y) = 4 - 5 = -1

Therefore, the coordinates of endpoint E are (2, -1).