Question

"Point B is the midpoint of segment AC. The coordinates of A are (-9, 3) and the coordinates of B are (2, -3). What are the coordinates of C?"

a) (13, 9)
b) (-13, -9)
c) (-5, 6)
d) (4, 0)

Answer 1

The coordinates of point C are found using the midpoint formula and by solving the resulting equations. The calculated coordinates of point C are (13, -9), which is answer option a.

Step-by-step explanation:

To find the coordinates of point C when point B is the midpoint of segment AC, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint, B, are the averages of the coordinates of points A and C. That is, if B is the midpoint of AC, then Bx = (Ax + Cx)/2 and By = (Ay + Cy)/2.

Given that point A has coordinates (-9, 3) and point B, the midpoint, has coordinates (2, -3), we can set up the following equations to find the coordinates of point C:

• Bx = (Ax + Cx)/2 => 2 = (-9 + Cx)/2
• By = (Ay + Cy)/2 => -3 = (3 + Cy)/2

Solving these equations gives us:

• Cx = 2 * 2 + 9 = 13
• Cy = -3 * 2 - 3 = -9

Therefore, the coordinates of point C are (13, -9), which corresponds to option a.