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Math Perspective Drawing Tasks

The document is an activity sheet that provides perspective drawing exercises for a mathematics course. It includes the following types of problems: [1] perspective drawing of points on a line; [2] perspective drawing of plane figures like tiles and hexagons using straight edges; [3] problems involving projective plane axioms and models; [4] problems involving the projection of lines; and [5] problems involving linear fractional functions and function composition. Students are instructed to select specific problems to complete from options provided under each category.

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Jessica Abuda
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180 views5 pages

Math Perspective Drawing Tasks

The document is an activity sheet that provides perspective drawing exercises for a mathematics course. It includes the following types of problems: [1] perspective drawing of points on a line; [2] perspective drawing of plane figures like tiles and hexagons using straight edges; [3] problems involving projective plane axioms and models; [4] problems involving the projection of lines; and [5] problems involving linear fractional functions and function composition. Students are instructed to select specific problems to complete from options provided under each category.

Uploaded by

Jessica Abuda
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Activity 4

Perspective

GROUP NO.: 1 Date Given: May 27, 2022 Rating: ______


Course/Year: BSED-Mathematics 2 Date Submitted: May 31, 2022
Members:
Caliwan, Farrah Grace M. Esquierdo, Christina F.
Garapan, Camille Joy A. Macasil, Genely R.

Refer to handout.

Perspective Drawing
Out of 3 items below, select 1 item.

𝑛
5.1.1 Show that the line from (─1, 1) to (n, 0) crosses the y-axis at y = 𝑛+1. Hence, the
1 2 3
perspective images of the points x = 0, 1, 2, 3,… are the points y = 0, , , ,….
2 3 4

Drawing with Straight edge alone


Out of 5 items below, select 2 items.

Consider the triangular tile shown shaded in Figure 5.9. Notice that this triangle could be
half of the quadrangular tile shown in Figure 5.7 (this is a hint).

1
5.2.1 Draw a perspective view of the plane filled with many copies of this tile.

5.2.2 Also, by deleting some lines in your solution to Exercise 5.2.1 create a perspective
view of the plane filled with congruent hexagons.

2
Projective Plane Axioms and there models
Out of 4 items below, select 2 item.

3
Projection
Out of 3 items below, select 1 item.

We know that such functions represent combinations of certain projections from lines to
parallel lines, but do they include any projection from a line to a parallel line?

5.5.3 Show that projection of a line, from any finite point P, onto a parallel line is
represented by a function of the form f (x) = ax + b.

Linear Fractional Functions


Out of 4 items below, select 2 items.

𝑎𝑥+𝑏 𝑎 𝑏𝑐−𝑎𝑑
The formula 𝑐𝑥+𝑑 = 𝑐 + 𝑐(𝑐𝑥+𝑑) gives an inkling why the condition ad – bc ≠ 0 is part of the
𝑎𝑥+𝑏 𝑎
definition of a linear fractional function: If ad – bc + 0, then = is a constant function, and
𝑐𝑥+𝑑 𝑐
hence it maps the whole line onto one point.

If we want to map the line onto another line, it is therefore necessary to have ad-bc ≠ 0. It is
𝑎𝑥+𝑏
also sufficient, because we can solve the equation y = 𝑐𝑥+𝑑 for x in that case.

𝑎𝑥+𝑏
5.6.1 Solve the equation y = for x, and note where your solution assumes ad – bc ≠ 0.
𝑐𝑥+𝑑

4
𝑎1 𝑥+𝑏1 𝑎2 𝑥+𝑏2 𝐴𝑥+𝐵
5.6.2 If f1 (x) = 𝑐1 𝑥+𝑑1 and f2 (x) = 𝑐2 𝑥+d2, compute f1 (f2 (x)), and verify that it is of the form 𝐶𝑥+𝐷.

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