If you want to make an object appear towering and imposing in a drawing, where would you position the horizon line? Explain how this positioning affects the perception of the object.
Given a building drawn in three-point perspective with two vanishing points on the horizon line and one above the horizon, explain how this perspective creates a bird’s-eye view. Provide calculations if necessary.
Given a shape with coordinates [latex](2,3), (4,5),\text{ and } (6,3)[/latex], find the equation of the line that reflects the shape over the y-axis.
Identify a famous building that features reflection symmetry and explain how this symmetry imparts a sense of balance and harmony. Provide mathematical details if applicable.
Given a six-pointed star, calculate the degrees of rotation symmetry and explain how this symmetry conveys movement and dynamism.
Provide an example of rotation symmetry in nature and calculate the degrees of rotation symmetry.
Determine the coordinates of a point [latex](x,y)[/latex] after a [latex]90^\circ[/latex] rotation counterclockwise about the origin
Given a wallpaper pattern that repeats every [latex]4[/latex] inches, calculate how many repetitions there will be on a wall that is [latex]12[/latex] feet long.
Design a pattern that uses translation symmetry and explain how the pattern is repeated in a straight line. Provide mathematical details if applicable.
In a design, the length of one side is [latex]5[/latex] units, and the corresponding side in a similar design is [latex]8[/latex] units. If another side in the first design is [latex]6[/latex] units, what is the corresponding length in the similar design?
If the shorter side of a golden rectangle is [latex]5[/latex] units, what is the length of the longer side?
If the width of a building facade is [latex]30[/latex] meters, calculate the height that would make the facade’s proportions adhere to the golden ratio.
Given a painting with dimensions [latex]24 \times 15[/latex] inches, determine if the proportions adhere to the golden ratio.
If a building’s facade is divided into three equal parts, with windows in the first and third sections, evaluate how this design principle aligns with the rule of thirds.