Reflection
Reflect the ordered pair, (9, -2), over the y-axis.
(-9,-2)
Rotation 180° about the origin
Z(−1, −5), K(−1, 0), C(1, 1), N(3, −2)
Z'(1, 5), K'(1, 0), C'(−1, −1), N'(−3, 2)
A square with side length 24 feet is reduced by a scale factor of 1/2. What is the area of the new triangle?
144 units2
Problem 1
1) a reflection followed by a rotation
A right-angled triangle has side lengths 13, 84, and x. Find the length of the longest side.
x=85
Parallelogram EFGH has vertices E(-4,-2), F(1,-2), G(0,-5), and H(-5,-5). If EFGH is reflected over y=-x, what are the coordinates of E'F'G'H'?
E'(2,4) F'(2,-1) G'(5,0) H'(5,5)
Rotation 90° clockwise about the origin
S(1, −4), W(1, 0), J(3, −4)
S'(−4, −1), W'(0, −1), J'(−4, −3)
A rectangle has a length of 5 inches and a width of 3 inches. It is enlarged by a scale factor of 6. What are the side lengths of the new rectangle?
Length: 30 inches
Width: 18 inches
Problem 2
2) a translation four units down followed by a reflection over the y-axis
What is the distance between (2,-2) and (6,1) on the coordinate plane?
5 units
Line Segment CD is reflected over the y-axis. What are the new coordinates of C and D?
C(-3,4) and D(-2,1)
C'(2,1)
D'(3,4)
Rotation 270° counterclockwise about the origin.
U(1, −2), W(0, 2), K(3, 2), G(3, −3)
U'(-2,-1) W'(2,0) K'(2,-3) G'(-3,-3)
A triangle with side lengths 3 cm, 4 cm, and 5 cm is enlarged by a scale factor of 4. What is the area of the new triangle?
96 cm2
Problem 3
3) line reflection followed by a translation
The bottom of a ladder must be placed 3 feet from a wall. The ladder is 10 feet long. How far above the ground does the ladder touch the wall? Round to the nearest hundredths place.
~9.54 feet
Square LMNO has vertices L(-5,-4), M(-3,-4), N(-5,-6), and O(-3,-6). If LMNO is reflected over y=-2, what are the coordinates of L'M'N'O'?
L'(-5,0) M'(-3,0) N'(-5,2) O'(-3,2)
Rotate (-3,-2) 60° counterclockwise about (1,2).
Please bring your answer on graph paper for Ms. Facchino to check.
Check.
A rectangle with the dimensions 10 cm by 15 cm is reduced by a scale factor of 1/5. What will be the perimeter of the reduced rectangle?
Problem 4
3) a rotation of 90° counterclockwise about the origin followed by a reflection over the y-axis
Find the distance between the points (4,7) and (1,–6). Round your answer to the nearest hundredth.
13.34 units
Triangle ABC has vertices A(-2,1), B(-2,4), and C(0,4). If ABC is reflected over x=1, what are the coordinates of A'B'C'?
A'(4,1) B'(4,4) C'(2,4)
Rotation 162° clockwise about (-1,-1).
A(-4,-4) B(-3,-4) C(-5,-5) D(-2,-5)
Please bring your answer on graph paper for Ms. Facchino to check.
Check.
Carly is eating a cookie in the shape of a square. The cookie has a length of 5 centimeters. She splits the cookie exactly in half down the middle and takes a bite. The bite she took was a reduction of the piece by a scale factor of 1/2. What were the side lengths of the bite she took?
Length: 2.5 centimeters
Width: 1.25 centimeters
Problem 5
2) a reflection over line l followed by a reflection over line m
A square has a diagonal lengths of 10 inches. What is the area of the square?
50 in2