Question

In the standard (2, 4) coordinate plane, the point (2, 1) is the midpoint of CD. Point Chas coordinates (6, 8). What are the coordinates of point D?

Answer 1

Since (2, 1) is the midpoint of CD, we can use the midpoint formula to find the coordinates of point D.

The midpoint formula states that the coordinates of the midpoint M between two points A and B are:

M = ((x_A + x_B)/2, (y_A + y_B)/2)

In this case, we know that point C has coordinates (6, 8), and the midpoint between C and D is (2, 1). Therefore, we can set up two equations using the midpoint formula:

(6 + x_D)/2 = 2 (for the x-coordinates)

(8 + y_D)/2 = 1 (for the y-coordinates)

Solving for x_D and y_D, we get:

6 + x_D = 4 => x_D = -2

8 + y_D = 2 => y_D = -6

Therefore, the coordinates of point D are (-2, -6).