Introduction to Three Dimensional Geometry: common misconceptions

If your child says… “A plane takes the name of the axis sticking out.”

Ask together

Does z run along the floor or stick out from it?

What’s true

The plane's name comes from the axes running along its surface.

If your child says… “Negative x tells me the octant.”

Ask together

Both II and VI have negative x, so which sign distinguishes them?

What’s true

An octant needs the signs of x, y and z together.

If your child says… “Reaching an axis makes just one coordinate zero.”

Ask together

On the x-axis, what distances remain from the XY- and ZX-planes?

What’s true

An axis requires both coordinates belonging to the other axes to be zero.

If your child says… “I add the three gaps to get the distance.”

Ask together

Does OP follow the edges through E and F?

What’s true

Adding edge lengths measures a bent route rather than the straight connection.

If your child says… “Adding squared lengths tests whether points are collinear.”

Ask together

Along a straight ruler, do lengths add or do their squares add?

What’s true

Collinearity needs lengths themselves to add; the square test checks a right angle.

If your child says… “Equal opposite sides make it a rectangle.”

Ask together

Are this shape's diagonals equal?

What’s true

For a simple quadrilateral in one plane, equal opposite sides establish only a parallelogram.

If your child says… “Equal distances from two points make a sphere.”

Ask together

Can P move along the YZ-plane while remaining equally far from A and B?

What’s true

A sphere fixes distance from one centre; here, the equal distances can vary.

If your child says… “The centroid is halfway between two vertices.”

Ask together

Do all the medians meet at AB's midpoint?

What’s true

Every vertex contributes equally to the centroid's x-, y- and z-coordinates.