Question 5(Multiple Choice Worth 1 points)

Question

(02.01 MC)

Triangle XYZ is shown on the coordinate plane.

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 + 4, y − 1) and then reflected across the y-axis to create triangle X″Y″Z″, what is the location of X″?

(8, 4)
(−5, 2)
(−8, 4)
(−9, 2)
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)

Trapezoid JKLM is shown on the coordinate plane.

Trapezoid JKLM on the coordinate plane with ordered pairs at J negative 2, 1, at K 1, 1, at L 3, negative 2, at M negative 4, negative 2.

If trapezoid JKLM is translated using the rule (x, y) → (x + 3, y − 3) and then translated using the rule (x, y) → (x + 1, y − 2) to create trapezoid J″K″L″M″, what is the location of L″?

(−4, 5)
(2, −4)
(7, −7)
(9, −6)
Question 8(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)
Question 9(Multiple Choice Worth 1 points)
(02.01 LC)

Which transformation represents a reflection over the x-axis?

(x, y) → (−x, y)
(x, y) → (x , −y)
(x, y) → (y, x)
(x, y) → (−y, x)
Question 10(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 0, 1, point B at negative 1, 0, point C at negative 2, 1, point D at negative 2, 3, point E at negative 1, 4, and point F at 0, 3.

x‒axis, y = x, x‒axis, y = x
y-axis, x‒axis, y-axis
x‒axis, y-axis, y-axis
y = x, x‒axis, y = x, y-axis

Answer 1

Here are the answers to your questions:

Question 5: To find the location of point X″ after the transformations:

1. Translate X(4, 5) using the rule (x, y) → (x + 4, y - 1):

   • New coordinates of X: (4 + 4, 5 - 1) = (8, 4)

2. Reflect across the y-axis, which changes the x-coordinate's sign:

   • New coordinates of X″: (−8, 4)

The answer is (−8, 4).

Question 6: To find the line of reflection between pentagons PQRST and P′Q′R′S′T′, you can observe that the reflections appear to change the sign of the y-coordinates and potentially change the x-coordinates as well. The given coordinates suggest a reflection about the line y = -x, but since we have positive and negative values, let's check further:

P (-4, 6) reflects to P' (6, -4), and checking other pairs leads to a consistent reflection relationship with both coordinates reversed.

Thus, the line of reflection is the line y = -x. However, since this option isn't directly given, it seems more like it reflects around a line different from the given choices.

It looks like x = 0 (y axis) might be the correct option due to symmetry in the y-direction.

Question 7: To find the location of L″ after the translations:

1. Translate L(3, -2) using the rule (x, y) → (x + 3, y - 3):

   • New coordinates of L: (3 + 3, -2 - 3) = (6, -5)

2. Translate again using (x, y) → (x + 1, y - 2):

   • (6 + 1, -5 - 2) = (7, -7)

The answer is (7, -7).

Question 8: To find the translation rule:

1. D (3, 5) to D' (-6, 2):
   • Change in x: -6 - 3 = -9
   • Change in y: 2 - 5 = -3

This gives the rule (x, y) → (x - 9, y - 3).

Question 9: The transformation that represents a reflection over the x-axis changes the sign of the y-coordinate:

• Thus, the answer is (x, y) → (x, -y).

Question 10: To determine the set of reflections that carry hexagon ABCDEF onto itself:

• Since it looks like the hexagon is symmetric with respect to both the x-axis and the y-axis, and there may be diagonal symmetries involved.

The correct combination that allows this symmetry would likely be:

• x-axis, y-axis, x-axis.

Feel free to ask if you have more questions or need any clarifications!