Final answer:
The coordinates of the point that divides the line segment CD two-thirds of the way from C to D are calculated using the section formula and are found to be (1, 2).
Step-by-step explanation:
To find the coordinates of the point that divides CD two-thirds of the way from C to D, we need to use the section formula in coordinate geometry which gives the coordinates of a point that divides a line segment internally in a given ratio. Assuming C has coordinates (7.4) and D has coordinates (-2, 1), we need to find the point P that divides CD in the ratio of 2:1 (since P is two-thirds of the way from C to D, hence C is to P as P is to D).
Using the section formula, the coordinates of point P (x, y) can be found using the following equations:
- The x-coordinate of P is: x = (mx2 + nx1)/(m + n), where m = 2, n = 1, x1 = 7, and x2 = -2.
- The y-coordinate of P is: y = (my2 + ny1)/(m + n), where m = 2, n = 1, y1 = 4, and y2 = 1.
Substituting the given values into the formulas:
- x = (2*(-2) + 1*7)/(2 + 1) = (-4 + 7)/3 = 3/3 = 1
- y = (2*1 + 1*4)/(2 + 1) = (2 + 4)/3 = 6/3 = 2
Therefore, the coordinates of the point that divides CD two-thirds of the way from C to D are (1, 2).