Descriptive geometry exercises

Construct the point A[3; 2; 4].

Construct the point B[−2; 3; 0]. Where is its front view?

Construct the point C[1; 0; 3].

Construct the point D[−3; 0; 0]. What is true of its projections?

Construct any point Q lying in quadrant II (above π₁, behind π₂).

Construct B, the mirror image of A[2; 3; 1.5] in π₁.

Construct the points A[−2; 1; 3], B[3; 4; 1] and the segment AB.

Construct the horizontal trace P and the frontal trace N of line p = AB.

Construct the traces P and N of p = AB. Notice which quadrant N lies in.

Through M draw the line q parallel to p = AB.

Construct a line q lying in the plane ρ(4; 3; 5) and passing through its point M.

Construct the horizontal and frontal traces of α(−3; 4; 5).

Through the point M of plane β = ABC draw the horizontal principal line h (parallel to π₁).

Through M[1; 1.5; 1.2] of plane β(5; 3; 4) draw the frontal principal line f (parallel to π₂).

Through M[1; 1; 1.5] of plane γ(4; 4; 3) draw the line of greatest slope s with respect to π₁.

The point A[2; 1; z] lies in the plane ρ(4; 4; 4). Construct it (find z).

Construct the plane σ through line p = AB and point M, and both of its traces.

The classic maturita task: three points, a vector, a line, a plane and an angle.

Construct the point X where line p = AB pierces the plane ρ(4; 3; 5).

Construct the point X where line p = MN meets triangle ABC. The visibility of p (dashed behind the triangle) is drawn automatically – check it in both views.

Find where p meets triangle ABC the classical way: the first projecting plane σ of p, the covering line k = σ ∩ ABC, then X = k ∩ p.

Construct the intersection line r of planes α(4; 3; 5) and β(−3; 4; 2).

Construct the intersection r of α(5; 4; 3) and β(−4; 3; 5) from the traces: R = meet of the horizontal traces, S = meet of the frontal traces, r = RS.

Through M draw a line q parallel both to the plane ρ(4; 3; 5) and to π₁.

Through M draw the plane σ parallel to ρ(3; 4; 2) and construct its traces.

Through M draw the plane ν perpendicular to p = AB and construct P = p ∩ ν.

Construct the second projecting plane σ of line b, and the point X where line a meets σ.

Plane ABC and point M – the normal and the distance.

The orthogonal projection of a point into a plane.

Line AB and plane PQR.

A plane through three points on the axes.

Construct a segment equal in length to AB (for instance by rotating it into π₁).

Classically: construct the first projecting plane σ of AB and rotate AB with it into π₁. The image (A)(B) has the true length.

Through M draw the perpendicular n to plane α and construct its foot F (where it meets α).

Find the distance of M from ρ(4; 5; 3): the normal n, its foot F, the segment MF and its true length d₀ in π₁.

From M draw the perpendicular n to p = AB, construct its foot P and the segment MP.

Construct the true shape of triangle ABC by rotating its plane into π₁.

Find the inclination of p = AB to π₁.

Find the inclination of ρ(4; 4; 2) to π₁ using the line of greatest slope through M.

Find the angle between p = AB and the plane ρ(4; 3; 5).

In the space triangle ABC construct the altitude from C: the line h ⟂ c (c = AB) and its foot P on c.

Through p = AB pass a plane σ perpendicular to ρ(4; 3; 5).

A cube and three points on its edges - find the section and its area.

Two skew lines and their distance.

The angle of two planes sharing a line.

A line and the plane z = 0.

Find the distance of α(4; 4; 4) and β(6; 6; 6): a common normal n, its meets A ∈ α, B ∈ β, the segment AB and its true length d₀ in π₁.

Construct the intersection line r of the planes of triangles ABC and KLM. Edge visibility is drawn automatically – check it agrees with r.

Through M draw the transversal q of the skew lines a, b – a line meeting both.

Construct the common perpendicular o of the skew lines a, b – a line meeting both at right angles.

The foot of the perpendicular and the distance.