10.5: Exercises
- Page ID
- 32004
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Identify the image of point P under the following transformations.
- a translation along vector
- a reflection across line l
- a counterclockwise rotation of 90° about point O
- A glide-reflection across l and along
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| l | A | |||||||||
| P | ||||||||||
- Identify the image of point P under the following transformations.
- a translation along vector
- a reflection across line l
- a counterclockwise rotation of 90° about point O
- A glide-reflection across l and along
| D | l | E | ||||||||
| O | C | |||||||||
| B | ||||||||||
| P | ||||||||||
| A |
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- Identify the image of point P under the following transformations.
- a translation along vector
- a reflection across line l
- a counterclockwise rotation of 90° about point O
- A glide-reflection across l and along
| F | C | |||||||||
| E |
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| O | P | |||||||||
| A | l | |||||||||
| B | ||||||||||
- Identify the image of point P under the following transformations.
- a translation along vector
- a reflection across line l
- a clockwise rotation of 90° about point O
- A glide-reflection across l and along
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| F |
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| O |
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- Identify the image of point P under the following transformations.
- a translation along vector
- a reflection across line l
- a clockwise rotation of 90° about point O
- A glide-reflection across l and along
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| E | ||||||||||
| P | l |
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- Translate the figure along vector
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- Translate the figure along vector
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- Translate the figure along vector
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- Translate the figure along vector
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- Rotate the figure 90° clockwise about the rotocenter R.
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- Rotate the figure 90° clockwise about the rotocenter R.
- Rotate the figure 180° clockwise about the rotocenter R.
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- Rotate the figure 180° clockwise about the rotocenter R.
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- Reflect the figure over the line l.
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- Reflect the figure over the line l.
- Reflect the figure over the line l.
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- Reflect the figure over the line l.
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- Glide-reflect the figure over the line l and along the vector
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- Glide-reflect the figure over the line l and along the vector
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- Glide-reflect the figure over the line l and along the vector
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- Glide-reflect the figure over the line l and along the vector
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- In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.
- b.
- In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.
- b.
- In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.
a. b.
- In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.
a. b.
- In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.
a. b.
- In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.
a. b.
- Enlarge the figure with respect to the point P by a factor of 2.
| P | ||||||||||
- Enlarge the figure with respect to the point P by a factor of 2.
| P | ||||||||||
- Enlarge the figure with respect to the point P by a factor of 2.
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- Enlarge the figure with respect to the point P by a factor of 2.
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- Shrink the figure with respect to the point P by a factor of
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- Shrink the figure with respect to the point P by a factor of
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| P |
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- Shrink the figure with respect to the point P by a factor of
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- Shrink the figure with respect to the point P by a factor of
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| P | ||||||||||
- Triangles A and
are similar and are related by the scale factor of 3.
- If the perimeter of triangle A is 12 ft, find the perimeter of
.
- If the area of triangle A is 8 ft2, find the area of
.
- If the perimeter of triangle A is 12 ft, find the perimeter of
- Triangles A and
are similar and are related by the scale factor of 4.
- If the perimeter of triangle A is 48 ft, find the perimeter of
.
- If the area of triangle A is 140 ft2, find the area of
.
- If the perimeter of triangle A is 48 ft, find the perimeter of
- Triangles A and
are similar and are related by the scale factor of 5.
- If the perimeter of triangle A is 42 ft, find the perimeter of
.
- If the area of triangle A is 68 ft2, find the area of
.
- If the perimeter of triangle A is 42 ft, find the perimeter of
- Triangles A and
are similar and are related by the scale factor of 2.
- If the perimeter of triangle A is 42 ft, find the perimeter of
.
- If the area of triangle A is 80 ft2, find the area of
.
- If the perimeter of triangle A is 42 ft, find the perimeter of
- The shapes A and
are similar.
A
8 18
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- If the perimeter of rectangle A is 22 ft, find the perimeter of
.
- If the area of rectangle A is 24 ft2, find the area of
.
- If the perimeter of rectangle A is 22 ft, find the perimeter of
- The shapes A and
are similar.
A
12
18
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- If the perimeter of triangle A is 32 ft, find the perimeter of
.
- If the area of triangle A is 48 ft2, find the area of
.
- If the perimeter of triangle A is 32 ft, find the perimeter of
- Find the value of x so that the red larger rectangle on the right is a gnomon to the blue smaller rectangle on the left.
10
4 x
- Find the value of x so that the red L-shape is a gnomon to the blue rectangle.
8
15
- Find the value of x so that the red triangle on the right is a gnomon to the blue triangle on the left.
9 9
6 x
- Find the values of x and y so that the red trapezoid is a gnomon to the blue triangle.
4 5
- Compute the values of the following.
- Compute the values of the following.
- Compute the values of the following using Binet’s simplified formula.
- Compute the values of the following using Binet’s simplified formula.
- Given
and
, find
and
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- Given
and
, find
and
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- Solve the quadratic equation
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- Solve the quadratic equation
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- Solve the quadratic equation
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- Solve the quadratic equation
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- Solve the quadratic equation
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- Solve the quadratic equation
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