Question

The midpoint of RS is M(6, 3). One endpoint is S(10, 4). Find the coordinates of the other endpoint R.

Write the coordinates as decimals or integers.
A) R(2, 1)
B) R(4, 2)
C) R(8, 5)
D) R(12, 6)

Answer 1

The coordinates of the other endpoint R are found by using the midpoint formula, which leads to the conclusion that the endpoint R should be R(2, 2), although it is not listed in the options. Among the given options, R(2, 1) is the closest to the calculated coordinates.

Step-by-step explanation:

To find the coordinates of the other endpoint R when given that the midpoint of RS is M(6, 3) and one endpoint is S(10, 4), we can use the midpoint formula. The midpoint M is the average of the x-coordinates and y-coordinates of the endpoints R and S.

The midpoint formula is given as:
M(x) = (R(x) + S(x)) / 2,
M(y) = (R(y) + S(y)) / 2.

Substitute the known values to find R(x) and R(y):
6 = (R(x) + 10) / 2,
3 = (R(y) + 4) / 2.

Solve for R(x) and R(y):
R(x) = 2 * 6 - 10 = 2,
R(y) = 2 * 3 - 4 = 2.

Therefore, the coordinates of the other endpoint R are R(2, 2), which is not in the options provided. This means there may have been a mistake in the options or in the given question. However, if we strictly consider the given options, R(2, 1) would be the closest to the calculated coordinates of R, with a slight discrepancy.