Question

The midpoint of segment CD has coordinates (5,6). Point C has coordinates (-5,-1). Find the coordinates of point D. Write in the format D(x,y)

Answer 1

To find the coordinates of point D given that the midpoint of segment CD is (5,6) and point C is (-5,-1), we use the midpoint formula in reverse, resulting in the coordinates D(10, 7).

Step-by-step explanation:

The midpoint formula in coordinate geometry states that the midpoint M of a segment with endpoints A(x1, y1) and B(x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2). Knowing that the midpoint of segment CD is (5,6) and point C has coordinates (-5,-1), we can find the coordinates of point D using this formula.

Let the coordinates of point D be D(x, y). Since (5,6) is the midpoint, we apply the midpoint formula in reverse to find x and y:

(5 + (-5))/2 = x/2 → x = 5 - (-5) → x = 10
(6 + (-1))/2 = y/2 → y = 6 - (-1) → y = 7

Therefore, the coordinates of point D are D(10, 7).