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100+ Free Canary Islands PAU Technical Drawing Applied to Plastic Arts & Design II Practice Questions
Canary Islands PAU Technical Drawing Applied to Plastic Arts and Design II (Dibujo Técnico Aplicado a las Artes Plásticas y al Diseño II 2º Bachillerato COPAU 2026) practice questions are available now; exam metadata is being verified.
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Sample Canary Islands PAU Technical Drawing Applied to Plastic Arts & Design II Practice Questions
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1In applied plane geometry, what is the fundamental condition for a circle to be tangent to a straight line at a specific point T?
A.The chord passing through T must be equal to half the circumference length.
B.The center of the circle must lie on a line parallel to the tangent line at distance equal to the diameter.
C.The center of the circle must lie on the perpendicular line to the tangent line erected at point T.
D.The radius drawn to point T must form an angle of 45° with the tangent line.
Explanation: By definition of tangency in plane geometry, the radius connecting the circle's center to the point of tangency T is strictly perpendicular to the tangent line at T. Therefore, the center of any tangent circle must lie along the normal (perpendicular) line drawn at T.
2In a geometric plane inversion defined by center O and positive power K, what is the inverse of a circle that passes through the center of inversion O?
A.A straight line not passing through the center of inversion O, perpendicular to the diameter connecting O to the circle's center.
B.Another circle of identical radius passing through the center of inversion O.
C.A straight line passing directly through the center of inversion O.
D.A parabola whose vertex is located at the center of inversion O.
Explanation: In plane inversion, any circle that passes through the inversion center O transforms into a straight line that does not pass through O. The resulting line is perpendicular to the line connecting O to the center of the original circle.
3When applying homothety with ratio k = -0.5 to scale a design module centered at O, how does the transformed module relate to the original?
A.It is translated by 0.5 units along the x-axis without changing size.
B.It is reduced to half its linear size and kept in the exact same orientation relative to O.
C.It is enlarged by a factor of 2 and kept in the same orientation relative to O.
D.It is inverted (rotated 180° relative to O) and reduced to half its original linear dimensions.
Explanation: A negative homothety ratio k = -0.5 scales all vectors from O by a factor of 0.5 in the opposite direction. This produces a 180° inverted figure reduced to 50% of its original linear dimensions.
4To construct a circular arc of given radius R tangent to two non-parallel intersecting lines, where must the center of the arc be located?
A.At the midpoint of the segment connecting the vertices of the two lines.
B.At the intersection of the angle bisector with the original lines.
C.On the perpendicular bisector of the line segment joining the two line endpoints.
D.At the intersection of two lines drawn parallel to the original lines at a distance R, lying on the bisector of the angle between them.
Explanation: The locus of points equidistant by radius R from a straight line consists of two parallel lines at distance R. Intersecting the parallel lines corresponding to both original lines places the center on the angle bisector at exact distance R from both lines.
5An ellipse used in industrial product design has a major axis 2a = 100 mm and a minor axis 2b = 60 mm. What is the focal distance 2c between its two foci F1 and F2?
A.80 mm
B.40 mm
C.70 mm
D.90 mm
Explanation: In an ellipse, the semi-axes a, b, and semi-focal distance c satisfy the Pythagorean relation a² = b² + c². Here a = 50 mm and b = 30 mm. Thus c = √(50² - 30²) = √(2500 - 900) = √1600 = 40 mm. The total focal distance 2c = 2 × 40 = 80 mm.
6What is the defining geometric locus property of a parabola applied in parabolic solar reflector design?
A.Every point on the parabola is equidistant from a fixed point (focus F) and a fixed line (directrix d).
B.The sum of the distances from any point on the curve to two fixed foci is constant.
C.The difference of the distances from any point on the curve to two fixed foci is constant.
D.The product of the distances from any point to two perpendicular axes is constant.
Explanation: By definition, a parabola is the locus of points in a plane whose distance to a fixed point (the focus F) equals its perpendicular distance to a fixed line (the directrix d). This property directs parallel incident rays to converge at the focus.
7In the design of a hyperbolic cooling structure, the hyperbola has semi-transverse axis a = 30 mm and semi-conjugate axis b = 40 mm. What are the equations of its asymptotes relative to the principal center axes?
A.y = ± (4/3) x
B.y = ± (3/4) x
C.y = ± (5/3) x
D.y = ± (3/5) x
Explanation: The asymptotes of a hyperbola with horizontal transverse axis 2a and vertical conjugate axis 2b centered at the origin are given by y = ± (b/a) x. Given a = 30 mm and b = 40 mm, the slope is b/a = 40/30 = 4/3, giving y = ± (4/3) x.
8In a plane inversion with center O and positive power K, a circle C does NOT pass through O. What is the nature and position of its inverted figure C'?
A.C' is a straight line parallel to the tangent line at O.
B.C' is another circle not passing through O, homothetic to C with respect to O, but its inverted center O' does not coincide with the inverse of C's center.
C.C' is an ellipse centered at O with major axis proportional to K.
D.C' is a parabolic arc tangent to the radical axis of inversion.
Explanation: An inversion transforms a circle not passing through the center of inversion O into another circle C' not passing through O. Under inversion, the center of C does not map to the center of C' (geometric center is not invariant under inversion).
9In an axial affinity transformation applied to alter a graphic logo, which property remains invariant for all corresponding points and line segments?
A.Circles always transform into identical congruent circles.
B.Distances between all arbitrary pairs of points are strictly preserved (isometric).
C.Angles between intersecting lines are preserved without distortion.
D.Parallelism between lines is preserved, and points on the affinity axis remain invariant (fixed).
Explanation: Axial affinity is an affine transformation that leaves all points on the affinity axis fixed and preserves parallelism between lines. However, it alters angles and distances, transforming circles into ellipses.
10In plane homology (central collinearity), what defines the vanishing line (línea límite) L of the original plane?
A.It is the locus of points whose homologous points lie at infinity; it is parallel to the homology axis.
B.It is the line connecting the homology center O to the origin of coordinates.
C.It is the line where homologous lines intersect at 90°.
D.It is the perpendicular bisector of the segment between O and the axis.
Explanation: In central homology, the vanishing line (línea límite L) is the line parallel to the homology axis containing all points whose homologous images are located at infinity. Conversely, L' in the homologous plane receives images of points at infinity.
About the Canary Islands PAU Technical Drawing Applied to Plastic Arts & Design II Practice Questions
Verified exam format metadata for Canary Islands PAU Technical Drawing Applied to Plastic Arts and Design II (Dibujo Técnico Aplicado a las Artes Plásticas y al Diseño II 2º Bachillerato COPAU 2026) is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.