Name: ____________________
Section: _______ Seat #: _______
Transformations
This activity develops understanding of transformations on graph paper. Work in pairs.
I. ∆ABC
1. Plot and label points A(1, 3), B(2, -3), and C(-2, 1) on graph paper. Draw ∆ABC.
2. Plot and label points A′(6, 3), B′(7, -3), and C′(3, 1) on the same grid. Draw
∆A′B′C′.
3. How are the coordinates of A′B′C′ related to the coordinates of A, B, and C?
4.
What transformation maps ∆ABC onto ∆A′B′C′?
5.
The coordinates of points A′′, B′′, and C′′ are formed from the coordinates of points
A, B, and C by adding 3 to the respective y-coordinates. Without plotting points,
predict the transformation that will map ∆ABC onto ∆A′′B′′C′′. Check your
prediction by finding the coordinates of points A′′, B′′, and C′′ and plotting the
points.
∆DEF is the translation image when ∆ABC is translated 4 units to the left and 2 units
down. Without performing the translation, how can you determine the coordinates
of points D, E, and F from the coordinates of points A, B, and C? Check your
answer by finding the coordinates of points D, E, and F and plotting the points.
6.
II. ∆GHJ
1. Plot and label points G(1, 6), H(3, 5), and J(4, 2) on graph paper. Draw ∆GHJ.
2. The coordinates of points G′, H′, and J′ are formed from the coordinates of G, H, and
J by multiplying the respective x-coordinates by -1. Find the coordinates of G′, H′,
and J′. Plot and label the points. Draw ∆G′H′J′. What transformation maps ∆GHJ
onto ∆G′H′J′?
3. What would you do to the coordinates of points G, H, and J to reflect ∆GHJ through
the x-axis? Check your answer by reflecting ∆GHJ through the x-axis and finding
the coordinates of the images of point G, H, and J.
III. ∆MNP
1. The vertices of a triangle are M(2, 6), N(4, 3), and P(1, 4), and the points M′(-2, -6),
N′(-4, -3), and P′(-1, -4) are their images under a transformation. Without plotting
points, predict what transformation maps ∆MNP onto ∆M′N′P′. Hint: This is the
composite of two transformations. Check your prediction by plotting the points.
2. ∆MNP is mapped onto ∆M′′N′′P′′ by reflecting ∆ through the y-axis and then
translating the image down 3 units (a glide reflection). Without performing the glide
reflection, find the coordinates of points M′′, N′′, and P′′. Check your answer by
performing the glide reflection and finding the coordinates of M′′, N′′, and P′′.
Name: ____________________
Section: _______ Seat #: _______
IV. ∆STU
1. Plot and label the points S(4, 1), T(4, 3), and U(7, 1) on graph paper. Draw ∆STU
2. Plot and label points S′(1, 4), T′(3, 4), and U′(1, 7) on the same grid. Draw
∆S′T′U′.
3. How are the coordinates of S′, T′, and U′ related to the coordinates of S, T, and U?
4.
What transformation maps ∆STU onto ∆S′T′U′?
5.
Plot and label points S′′(-1, -4), T′′(-3, -4), and U′′(-1, -7) on the same grid. Draw
∆S′′T′′U′′.
How are the coordinates of points S′′, T′′, and U′′ related to the coordinates of S,
T, and U?
6.
7.
V.
What transformation maps ∆STU onto ∆S′′T′′U′′?
Reflections and Summary
1. What single transformation has the same effect as reflecting a triangle through the
line y = x and then reflecting the image through the x-axis?
2. If the coordinates of the vertices of the triangle are (a, b), (c, d), and (e, f), what
are the coordinates of the images of the vertices under this transformation? Check
your answers by drawing a triangle and performing the reflections.
3. What happens to a triangle when the coordinates of its vertices are multiplied by a
positive number?
Name: ____________________
Section: _______ Seat #: _______
Name: ____________________
Section: _______ Seat #: _______