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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

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

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

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

View image calculista

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