Respuesta :

meerkat18
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)
calculista

we have

[tex] A(-3,6) \\ B(6,-3) [/tex]

Step [tex] 1 [/tex]

Find the distance AB in the x-coordinate

[tex] dABx=6-(-3)\\ dAB=9units [/tex]

Step [tex] 2 [/tex]

Find the distance AB in the y-coordinate

[tex] dABy=6-(-3)\\ dAB=9units [/tex]

Step [tex] 3 [/tex]

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

[tex] Cx=Ax+\frac{dABx}{3}\\ \\ Cx=-3+\frac{9}{3}\\ \\ Cx=0 [/tex]

[tex] Dx=Cx+\frac{dABx}{3}\\ \\ Dx=0+\frac{9}{3}\\ \\ Dx=3 [/tex]

Step [tex] 4 [/tex]

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

[tex] Cy=Ay-\frac{dABx}{3}\\ \\ Cy=6-\frac{9}{3}\\ \\ Cy=3 [/tex]

[tex] Dy=Cy-\frac{dABx}{3}\\ \\ Dy=-3-\frac{9}{3}\\ \\ Dy=0 [/tex]

therefore

point [tex] C(0,3) [/tex]

point [tex] D(3,0) [/tex]

see the attached figure

the answer is

the coordinates are

[tex] C(0,3)\\D(3,0) [/tex]

Ver imagen calculista