Questions: Select the correct answer. In the diagram, C and D are located such that AB is divided into three equal parts. What are the coordinates of C and D? A. C(1,3), D(3,1) B. C(-3,0), D(3,-6) C. C(0,3), D(3,0) D. C(-1.5,3), D(1.5,0)

Solution Steps

The x-coordinate of A is -3 and the x-coordinate of B is 6. The difference is 6 - (-3) = 9.

The y-coordinate of A is 6 and the y-coordinate of B is -3. The difference is -3 - 6 = -9.

Since the line segment AB is divided into three equal parts, we divide the differences by 3.

Difference in x-coordinates divided by 3: 9 / 3 = 3

Difference in y-coordinates divided by 3: -9 / 3 = -3

C is one-third of the way from A to B. So, we add the values calculated in Step 2 to the coordinates of A.

x-coordinate of C: -3 + 3 = 0 y-coordinate of C: 6 + (-3) = 3 Therefore, C = (0, 3)

D is two-thirds of the way from A to B. We can find D's coordinates by adding twice the values calculated in Step 2 to the coordinates of A or by adding the values calculated in step 2 to C's coordinates. x-coordinate of D: 0 + 3 = 3 y-coordinate of D: 3 + (-3) = 0 Therefore, D = (3, 0)

Final Answer