1103059602 | math4u.vsb.cz

SubArea:

Positional properties

Level:

Project ID:

1103059602

Source Problem:

Accepted:

1

Clonable:

1

Easy:

0

Let

A B C D V

be a rectangle based-pyramid and

V

its apex. The pyramid is sliced by a plane

X Y Z

which is defined by:

\begin{aligned} X & is the midpoint of  the edge A D, \\ Y & \in C D \land | D Y | = 3 | C Y |, \\ Z & \in B V \land | B Z | = 3 | V Z | \end{aligned}

(see the picture). What is the cross-section of the pyramid if we slice it with the plane

X Y Z

?

a pentagon

X Y K Z L

with points

K

and

L

lying on the edges

C V

and

A V

a triangle

X Y Z

a quadrilateral

X Y Z L

with point

L

lying on the edge

A V

a quadrilateral

X Y K Z

with point

K

lying on the edge

C V