3D Section Formula Practice Problems Online

What are the coordinates of $P$ which divide the line segment joining the points $A=(-4,4,1)$ and $B=(4,-4,2)$ in the ratio $3:2 ?$

\left(\frac{4}{5},\frac{4}{5},\frac{8}{5}\right)

\left(\frac{4}{5},-\frac{4}{5},\frac{8}{5}\right)

\left(\frac{8}{5},-\frac{8}{5},\frac{8}{5}\right)

\left(\frac{8}{5},\frac{8}{5},\frac{8}{5}\right)

Let $A ( 4, 3, 5 )$ and $B ( 2, 6 , 0)$ be two fixed points. Find the position vector of the point which lies on the line segment $\overline{AB}$ and internally divides it in the ratio $7 : 8.$

\left( \frac{16}{5} , \frac{24}{5} , \frac{8}{3}\right)

\left( \frac{6}{5} , \frac{-6}{5} , \frac{8}{3}\right)

\left( \frac{46}{15} , \frac{22}{5} , \frac{8}{3}\right)

\left( \frac{-6}{5} , \frac{6}{5} , \frac{-8}{3}\right)

The above rectangular cuboid has base dimensions $a=12$ and $b=8.$ If the centroid $I$ of triangle $ACF$ internally divides the diagonal $\overline{BH}$ of the rectangular cuboid in the ratio $BI:IH=1:m,$ what is the value of $m?$

Suppose three vertices of a parallelogram are $O=(0,0,0), A=(1,5,6), B=(-1,-5,5),$ where $\overline{OA}$ and $\overline{OB}$ are adjacent sides. If $C$ is the final vertex of the parallelogram, then what are the coordinates of $C ?$

Consider a triangle $ABC$ such that the centroid of of the triangle is $G=(5,-2,3)$ and the midpoint of $\overline{AB}$ is $P=\left(1,\frac{1}{2},\frac{1}{2}\right).$ What are the coordinates of the point $C ?$

Concept Quizzes

Challenge Quizzes

3D Section Formula

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.