Question

In Line JG, with the midpoint at M (-2, 6) and M (12, 10), what are the coordinates of the other endpoint G?

A) G (26, 14)
B) G (32, 16)
C) G (8, 4)
D) G (10, 12)

Answer 1

The coordinates of the other endpoint G are (12, 10).

Step-by-step explanation:

Let's use the midpoint formula to find the coordinates of point G. The midpoint formula states that the coordinates of the midpoint (M) between two endpoints (J and G) is given by:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

Plugging in the given coordinates for M (-2, 6) and the other endpoint (12, 10), we get:

M = ((-2 + 12) / 2, (6 + 10) / 2)

M = (10 / 2, 16 / 2)

M = (5, 8)

So, the coordinates of point G will be the same as point J but reflected across the midpoint: G (2 * 5 - xJ, 2 * 8 - yJ)

Plugging in the coordinates of M (-2, 6) and J, we get:

G = (2 * 5 - (-2), 2 * 8 - 6)

G = (10 + 2, 16 - 6)

G = (12, 10)

Therefore, the coordinates of the other endpoint G are (12, 10), which corresponds to answer choice D).