Triangle XYZ on the coordinate plane with ordered pairs at X 4, 5, at Y 5, 3, at Z 1, 3
If triangle XYZ is translated using the rule (x, y) → (x + 1, y − 4) and then reflected across the x-axis to create triangle X″Y″Z″, what is the location of Y″?
(−1, 6)
(2, 1)
(5, −1)
(6, 1)
Question 5
(Multiple Choice Worth 1 Points)
(02.01 LC)
Trapezoid JKLM is shown on the coordinate plane below:
Trapezoid JKLM on the coordinate plane with ordered pairs at J negative 7, negative 2, at K negative 4, negative 2, at L negative 2, negative 5, at M negative 9, negative 5.
If trapezoid JKLM is translated according to the rule (x, y) → (x + 8, y − 3), what are the coordinates of point L′?
(1, −5)
(−10, 6)
(−5, 3)
(6, −8)
Question 6
(Multiple Choice Worth 1 Points)
(02.01 LC)
Pentagon PQRST and its reflection, pentagon P′Q′R′S′T′, are shown in the coordinate plane below:
Pentagon PQRST and pentagon P prime Q prime R prime S prime T prime on the coordinate plane with ordered pairs at P negative 4, 6, at Q negative 7, 4, at R negative 6, 1, at S negative 2, 1, at T negative 1, 4, at P prime 6, negative 4, at Q prime 4, negative 7, at R prime 1, negative 6, at S prime 1, negative 2, at T prime 4, negative 1.
What is the line of reflection between pentagons PQRST and P′Q′R′S′T′?
y = x
y = 0
x = 1
x = 0
Question 7
(Multiple Choice Worth 1 Points)
(02.01 MC)
What set of reflections would carry hexagon ABCDEF onto itself?
Hexagon ABCDEF on the coordinate plane with point A at 1, 0, point B at 0, 1, point C at 1, 2, point D at 3, 2, point E at 4, 1, and point F at 3, 0.
y = x, x‒axis, y = x, y-axis
x‒axis, y = x, x‒axis, y = x
y-axis, x‒axis, y-axis
x‒axis, y-axis, y-axis
Question 8
(Multiple Choice Worth 1 Points)
(02.01 MC)
A triangle has vertices at B(−3, 0), C(2, −1), D(−1, 2). Which transformation would produce an image with vertices B″(1, −2), C″(0, 3), D″(3, 0)?
(x, y) → (x + 1, y + 1) → (y, x)
(x, y) → (x + 1, y + 1) → (−x, y)
(x, y) → (x, −y) → (x + 2, y + 2)
(x, y) → (−x, y) → (x + 2, y + 2)
Question 9
(Multiple Choice Worth 1 Points)
(02.01 MC)
Pentagon ABCDE and pentagon A″B″C″D″E″ are shown on the coordinate plane below:
Pentagon ABCDE and pentagon A double prime B double prime C double prime D double prime E double prime on the coordinate plane with ordered pairs at A negative 5, negative 2, at B negative 7, negative 3, at C negative 6, negative 6, at D negative 3, negative 5, at E negative 3, negative 3, at A prime 3, 6, at B prime 5, 5, at C prime 4, 2, at D prime 1, 3, at E prime 1, 5.
Which two transformations are applied to pentagon ABCDE to create A″B″C″D″E″?
Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the y-axis
Translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the x‒axis
Translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the y-axis
Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the x‒axis
Question 10
(Multiple Choice Worth 1 Points)
(02.01 MC)
Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′:
Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D are 3, 5, at E 7, 5, at F 8, 2, at G 7, negative 1, at H 3, negative 1, at I 2, 2; at D prime negative 6, 2, at E prime negative 2, 2, at F prime negative 1, negative 1, at G prime negative 2, negative 4, at H prime negative 6, negative 4, at I prime negative 7, negative 1
Which rule represents the translation of hexagon DEFGHI to hexagon D′E′F′G′H′I′?
(x, y) → (x − 9, y − 3)
(x, y) → (x − 3, y − 9)
(x, y) → (x + 3, y + 3)
(x, y) → (x + 9, y + 9)
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1 answer
Let’s break down each question one by one:
Question 4: What is the location of Y″ after the transformations?
Start with point Y(5, 3).
Apply the translation using the rule (x, y) → (x + 1, y - 4):
New coordinates: (5 + 1, 3 - 4) = (6, -1).
Reflect across the x-axis: (x, y) → (x, -y):
Y″ = (6, -(-1)) = (6, 1).
Answer: (6, 1)
Question 5: What are the coordinates of point L′ after the translation?
Start with point L(-2, -5).
Translate using the rule (x, y) → (x + 8, y - 3):
New coordinates: (-2 + 8, -5 - 3) = (6, -8).
Answer: (6, -8)
Question 6: What is the line of reflection between the pentagons?
The coordinates of points P and P′, and others, indicate that the reflection is symmetrical over the line y = -x.
Thus we look for consistency where if (x, y) reflects to (y, x).
Answer: y = x
Question 7: What set of reflections would carry hexagon ABCDEF onto itself?
To maintain symmetry, the hexagon would need to reflect over axes that switch coordinates in a way that they match original coordinates back again in their original arrangement:
The first reflection can be along y = x, then the second along the x-axis, which almost duplicates the arrangement leading to reflection over the y-axis bringing it back again.
Answer: y = x, x-axis, y = x, y-axis
Question 8: Which transformation would produce the specified image vertices?
Start with B(−3, 0), C(2, −1), D(−1, 2).
Transforming (x, y) → (x + 1, y + 1) will shift coordinates and make them positive, then the transformation (y, x) switches them:
B becomes (1, -2)
C becomes (0, 3)
D becomes (3, 0)
Answer: (x, y) → (x + 1, y + 1) → (y, x)
Question 9: Which transformations are applied to create A″B″C″D″E″?
By analyzing the coordinates:
A through E are transformed directly to A prime through E prime: likely a translation followed by a reflection across the y-axis to match the resulting coordinates.
Answer: Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the y-axis
Question 10: Which rule represents the translation from hexagon DEFGHI to D′E′F′G′H′I′?
Compare the coordinates' movement from points D and E to D′ and E′: (D=3,5 to D=-6,2 and E=7,5 to E=-2,2).
The translation results in:
Moving both D and E horizontally left significantly, and vertically down.
Answer: (x, y) → (x - 9, y - 3)
For each of your questions, I've provided a concise method to arrive at the answers. If you have further questions or need clarifications, feel free to ask!
