⁦Coordinates of a point in space⁩

⁦Topic from the Ukrainian Grade 10 textbook (algebra and calculus with geometry), section 6⁩ "⁦Coordinates and vectors in space⁩", ⁦item 38⁩ "⁦Cartesian coordinates of a point in space⁩". ⁦A rectangular coordinate system in space is three pairwise perpendicular number lines through one origin O⁩: ⁦the x-axis (abscissa axis), the y-axis (ordinate axis) and the z-axis (applicate axis)⁩. ⁦The planes through pairs of axes are the coordinate planes xy, xz and yz⁩. ⁦Every point M gets an ordered triple (x; y; z), written M (x; y; z)⁩.

⁦Distance theorem⁩: ⁦the distance between A (x₁; y₁; z₁) and B (x₂; y₂; z₂) is AB = √((x_٢ − x_١)^٢ + (y_٢ − y_١)^٢ + (z_٢ − z_١)^٢)⁩. ⁦Midpoint theorem⁩: ⁦the midpoint of AB has coordinates equal to the halves of the sums of the matching coordinates of the ends⁩. ⁦M (x; y; z) and N (x; y; −z) are symmetric about the plane xy; A (x; y; z) and B (−x; −y; −z) are symmetric about the origin⁩.

⁦The figure on the screen is only a box that shows how the coordinates of a point fix its position; the child types the answers⁩.