Translations
A point is located at P(3,4) on a coordinate plane. If you translate the point 5 units to the left and 2 units down, what are the new coordinates of the point, P′?
P′=(−2,2)
A point is located at A(4,7) on a coordinate plane. What are the coordinates of its image, A′, after a reflection over the y-axis?
A′=(−4,7)
A point is located at B(3,5) on a coordinate plane. What are the coordinates of its image, B′, after a 90° clockwise rotation about the origin?
B′=(5,−3)
A point is located at C(3,2) on a coordinate plane. What are the coordinates of its image, C′, after a dilation from the origin with a scale factor of 5?
C′=(15,10)
A point is located at P(2,3). First, it's translated 4 units to the right and 2 units down to create the image P′. Then, P′ is reflected over the x-axis to create the final image P′′. What are the coordinates of P′′
P′′=(6,−1)
Triangle XYZ has vertices at X(1,2), Y(4,5), and Z(5,1). Find the coordinates of the vertices of the image, triangle X′Y′Z′, after a translation of 3 units to the right and 4 units up.
X′=(4,6)
Y′=(7,9)
Z′=(8,5)
A rectangle has vertices at Q(1,1), R(1,4), S(6,4), and T(6,1). Find the coordinates of the vertices of the image, rectangle Q′R′S′T′, after a reflection over the x-axis.
Q′=(1,−1)
R′=(1,−4)
S′=(6,−4)
T′=(6,−1)
Triangle CAT has vertices at C(2,2), A(5,5), and T(5,2). Find the coordinates of the vertices of the image, triangle C′A′T′, after a 180° rotation about the origin.
C′=(−2,−2)
A′=(−5,−5)
T′=(−5,−2)
A trapezoid has vertices at A(4,8), B(10,8), C(12,4), and D(2,4). Find the coordinates of the vertices of the image, A′B′C′D′, after a dilation from the origin with a scale factor of 1/2.
A′=(2,4)
B′=(5,4)
C′=(6,2)
D′=(1,2)
A square has a vertex at A(−1,4). The square undergoes three transformations in order:
A 90° clockwise rotation about the origin.
A reflection over the y-axis.
A dilation from the origin with a scale factor of 2.
What are the final coordinates of the vertex, A′′′?
A′′′=(−8,2)
A line segment AB is translated to create the image A′B′. The original coordinates were A(−5,8) and the new coordinates are A′(2,4). Describe the translation in words and write a rule for it in the form (x,y)→(x+a,y+b).
(x+7,y−4).
The point P(5,−8) is reflected to create an image at P′(5,8). Was the line of reflection the x-axis or the y-axis?
reflection is over the x-axis
A point K(−2,7) is rotated about the origin to create an image at K′(−7,−2). Describe the rotation in degrees and direction (clockwise or counterclockwise).
The rotation was 90° counterclockwise about the origin.
A line segment PQ is dilated from the origin to create the image P′Q′. The original coordinates of one endpoint were P(4,−6) and the new coordinates are P′(6,−9). What was the scale factor of the dilation?
The scale factor was 1.5 (or 3/2).
Point B(3,1) is transformed to the final image B′′(−3,−4). Describe a possible two-step sequence of transformations that could make this happen using first a rotation and then a translation.
A possible sequence is: a 180° rotation about the origin, followed by a translation of 3 units down.
A parallelogram was translated according to the rule (x,y)→(x−6,y+3). After the translation, one of the vertices of the image is at C′(1,−2). What were the original coordinates of that vertex, C?
C=(7,−5)
Point W(−2,6) is first reflected over the y-axis to create point W′. Then, point W′ is translated 5 units down to create point W′′. What are the coordinates of the final point, W′′?
W′′=(2,1)
Point J(4,1) is first rotated 90° clockwise about the origin to create point J′. Then, point J′ is translated 6 units to the left to create point J′′. What are the coordinates of the final point, J′′?
J′′=(−5,−4)
A triangle was dilated from the origin with a scale factor of 7. After the dilation, one of the vertices of the image is at M′(14,−35). What were the original coordinates of that vertex, M?
M=(2,−5)
A point, M, was transformed to create the image M′′(−12,5). The sequence of transformations was:
A translation of 2 units left and 1 unit down.
A dilation from the origin with a scale factor of 3.
What were the original coordinates of point M?
M=(−2,8/3)
A point M(x,−3) is translated 4 units to the right and 5 units up. Its image, M′, has coordinates (1,y). Find the values of x and y.
M=(−3,−3)
A triangle has a vertex at F(−3,y). After a reflection over the x-axis, the corresponding vertex of the image is at F′(x,5). Find the values of x and y.
F=(−3,−5)
A point Q(x,−4) is rotated 90° counterclockwise about the origin. Its image, Q′, has coordinates (4,6). Find the values of x and y if the image was actually Q′(y,6). Find the value of x.
Q=(6,−4)
A point T(x,8) is dilated from the origin with a scale factor of 4. Its image, T′, has coordinates (12,y). Find the values of x and y.
T=(3,8)
Point Z(4,y) is transformed by a sequence. First, it's reflected over the x-axis to create Z′. Then, Z′ is rotated 90° counterclockwise about the origin to create the final point Z′′(5,x). Find the values of x and y.
y=5 and x=4