5. In the diagram at the right, the grid lines are 1 unit apart. Let T denote the affine transformation in R2 that maps the 4x2 shaded rectangle centred at the origin onto the 2x4 rectangle centred at (4, 4). Suppose that over the time interval 0 stsl every point (x, y) moves in a straight line at constant speed to its image T(x, y). [Different points can have different distances to travel so they will move at different speeds.] Note: There are many ways to solve this problem. I gave it recently to a few grade 9 students and they came up with a simple approach. Sometimes it's not good to know too much.] (a), rectangle becomes a line segment. There is one time t at which the moving Find the time at which this happens and make a careful drawing of this line segment on the diagram at the right. Here's a diagram you can use as a thinking pad.
5. In the diagram at the right, the grid lines are 1 unit apart. Let T denote the affine transformation in R2 that maps the 4x2 shaded rectangle centred at the origin onto the 2x4 rectangle centred at (4, 4). Suppose that over the time interval 0 stsl every point (x, y) moves in a straight line at constant speed to its image T(x, y). [Different points can have different distances to travel so they will move at different speeds.] Note: There are many ways to solve this problem. I gave it recently to a few grade 9 students and they came up with a simple approach. Sometimes it's not good to know too much.] (a), rectangle becomes a line segment. There is one time t at which the moving Find the time at which this happens and make a careful drawing of this line segment on the diagram at the right. Here's a diagram you can use as a thinking pad.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![5. In the diagram at the right, the grid lines are 1 unit
apart. Let T denote the affine transformation in R2
that maps the 4x2 shaded rectangle centred at the
origin onto the 2x4 rectangle centred at (4, 4).
Suppose that over the time interval 0 sts 1 every
point (x, y) moves in a straight line at constant speed
to its image T(x, y). [Different points can have
different distances to travel so they will move at
different speeds.]
Note: There are many ways to solve this problem. I
gave it recently to a few grade 9 students and they
came up with a simple approach. Sometimes it's not
good to know too much.]
(a),
rectangle becomes a line segment.
There is one time t at which the moving
Find the time at which this happens and make a
careful drawing of this line segment on the diagram at
the right.
Here's a diagram you can use as a thinking
pad.
CS Scanned with CamScanner](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6b572ef-c150-472a-b31d-8f512ee37557%2F48912fd2-b0a4-4fbf-814e-bd86b5aabebb%2F90ch5bl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. In the diagram at the right, the grid lines are 1 unit
apart. Let T denote the affine transformation in R2
that maps the 4x2 shaded rectangle centred at the
origin onto the 2x4 rectangle centred at (4, 4).
Suppose that over the time interval 0 sts 1 every
point (x, y) moves in a straight line at constant speed
to its image T(x, y). [Different points can have
different distances to travel so they will move at
different speeds.]
Note: There are many ways to solve this problem. I
gave it recently to a few grade 9 students and they
came up with a simple approach. Sometimes it's not
good to know too much.]
(a),
rectangle becomes a line segment.
There is one time t at which the moving
Find the time at which this happens and make a
careful drawing of this line segment on the diagram at
the right.
Here's a diagram you can use as a thinking
pad.
CS Scanned with CamScanner
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