Question

In the diagram, C and D are located such that AB is divided into 3 equal parts.

What are the coordinates of C and D?

Answer 1

we are given with a line segment that has endpoints at (-3,6) and (6,-3). The line segment is divided into three parts and is asked to determine the points in between the endpoints. x has a total length of -9, so C should have x-coordinate of 0 and D should have 3. Meanwhile, y has a total length of -9, so c's y should be 3 while D should have 0. so, C(0,3) and D (3,0)

Answer 2

we have

$A(-3,6) \\ B(6,-3)$

Step $1$

Find the distance AB in the x-coordinate

$dABx=6-(-3)\\ dAB=9units$

Step $2$

Find the distance AB in the y-coordinate

$dABy=6-(-3)\\ dAB=9units$

Step $3$

Find the coordinate of points C and D in the x-coordinate

Let

Cx------> x coordinate of point C

Dx------> x coordinate of point D

Ax------> x coordinate of point A

$Cx=Ax+\frac{dABx}{3}\\ \\ Cx=-3+\frac{9}{3}\\ \\ Cx=0$

$Dx=Cx+\frac{dABx}{3}\\ \\ Dx=0+\frac{9}{3}\\ \\ Dx=3$

Step $4$

Find the coordinate of points C and D in the y-coordinate

Let

Cy------> y coordinate of point C

Dy------> y coordinate of point D

Ay------> y coordinate of point A

$Cy=Ay-\frac{dABx}{3}\\ \\ Cy=6-\frac{9}{3}\\ \\ Cy=3$

$Dy=Cy-\frac{dABx}{3}\\ \\ Dy=-3-\frac{9}{3}\\ \\ Dy=0$

therefore

point $C(0,3)$

point $D(3,0)$

see the attached figure

the answer is

the coordinates are

$C(0,3)\\D(3,0)$