Question

|a - i| = 37 (in the third quadrant). T(10,15) is the midpoint of CD. The coordinates of D are (10,22). What are the coordinates of C?

Answer 1

The coordinates of point C can be found by using the midpoint formula and are (10, 8).

Step-by-step explanation:

The student is being asked to determine the coordinates of point C given that T(10,15) is the midpoint of line segment CD and the coordinates of D. Since T is the midpoint, the coordinates of C can be found by using the midpoint formula, which states that the midpoint T(x,y) can be calculated by taking the average of the x-coordinates and the average of the y-coordinates of C and D.

To find the x-coordinate of C, apply the midpoint formula:

Cx = 2 * Tx - Dx

Cx = 2 * 10 - 10

Cx = 20 - 10

Cx = 10

To find the y-coordinate of C, apply the midpoint formula:

Cy = 2 * Ty - Dy

Cy = 2 * 15 - 22

Cy = 30 - 22

Cy = 8

Therefore, the coordinates of point C are (10, 8).