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 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+(dABx)/(3)\\ \\ Cx=-3+(9)/(3)\\ \\ Cx=0`

`Dx=Cx+(dABx)/(3)\\ \\ Dx=0+(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-(dABx)/(3)\\ \\ Cy=6-(9)/(3)\\ \\ Cy=3`

`Dy=Cy-(dABx)/(3)\\ \\ Dy=-3-(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)`

Answer 2

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)