Question
Figure ABCDEF was reflected across the line y = –x to create figure A'B'C'D'E'F'.
On a coordinate plane, a 6-sided figure has points A prime (negative 2, negative 2), B prime (negative 4, 2), C prime (negative 2, 6), D prime (4, 6), E prime (6, 2), and F prime (4, negative 2).
What are the coordinates of the pre-image of F'?
(–2, 4)
(4, 2)
(2, –4)
(–4, –2)
On a coordinate plane, a straight line and a parallelogram are shown. The straight line has a positive slope and has a formula of y = x. The parallelogram has points E (3, negative 3), F (5, negative 3), H (2, negative 5), and G (4, negative 5).
What are the coordinates of the image of vertex G after a reflection across the line y = x?
(–4, –5)
(4, 5)
(–5, 4)
(5, –4)
On a coordinate plane, 2 triangles are shown. The first triangle has points M (negative 5, 4), N (negative 2, 3), and L (negative 4, 2). The second triangle has points L prime (negative 4, negative 2), M prime (negative 5, negative 4), and N prime (negative 2, negative 3).
What is the rule for the reflection?
rx-axis(x, y) → (–x, y)
ry-axis(x, y) → (–x, y)
rx-axis(x, y) → (x, –y)
ry-axis(x, y) → (x, –y)
ΔA'B'C' was constructed using ΔABC and line segment EH.
2 triangles are shown. Line E H is the line of reflection. Line segment B B prime has a midpoint at point D. Line segment A A prime has a midpoint at point F. Line segment C C prime has a midpoint at point G.
For to be the line of reflection between and , which statements must be true? Select three options.
BD = DB'
DF = FG
m∠EFA = 90°
The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
ΔABC is not congruent to ΔA'B'C'.
2 triangles are shown. Line M N is the line of reflection. Line segment X prime X has a midpoint at point A. Line segment Z prime Z has a midpoint at point B. Line segment Y prime Y has a midpoint at point C.
Which statements must be true about the reflection of ΔXYZ across Line M N? Select three options.
m∠X'Z'Y' = 90°
m∠MCY = 90°
XX' ≅ YY'
BZ' ≅ BZ
XY || X'Y'
On a coordinate plane, a 6-sided figure has points A prime (negative 2, negative 2), B prime (negative 4, 2), C prime (negative 2, 6), D prime (4, 6), E prime (6, 2), and F prime (4, negative 2).
What are the coordinates of the pre-image of F'?
(–2, 4)
(4, 2)
(2, –4)
(–4, –2)
On a coordinate plane, a straight line and a parallelogram are shown. The straight line has a positive slope and has a formula of y = x. The parallelogram has points E (3, negative 3), F (5, negative 3), H (2, negative 5), and G (4, negative 5).
What are the coordinates of the image of vertex G after a reflection across the line y = x?
(–4, –5)
(4, 5)
(–5, 4)
(5, –4)
On a coordinate plane, 2 triangles are shown. The first triangle has points M (negative 5, 4), N (negative 2, 3), and L (negative 4, 2). The second triangle has points L prime (negative 4, negative 2), M prime (negative 5, negative 4), and N prime (negative 2, negative 3).
What is the rule for the reflection?
rx-axis(x, y) → (–x, y)
ry-axis(x, y) → (–x, y)
rx-axis(x, y) → (x, –y)
ry-axis(x, y) → (x, –y)
ΔA'B'C' was constructed using ΔABC and line segment EH.
2 triangles are shown. Line E H is the line of reflection. Line segment B B prime has a midpoint at point D. Line segment A A prime has a midpoint at point F. Line segment C C prime has a midpoint at point G.
For to be the line of reflection between and , which statements must be true? Select three options.
BD = DB'
DF = FG
m∠EFA = 90°
The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
ΔABC is not congruent to ΔA'B'C'.
2 triangles are shown. Line M N is the line of reflection. Line segment X prime X has a midpoint at point A. Line segment Z prime Z has a midpoint at point B. Line segment Y prime Y has a midpoint at point C.
Which statements must be true about the reflection of ΔXYZ across Line M N? Select three options.
m∠X'Z'Y' = 90°
m∠MCY = 90°
XX' ≅ YY'
BZ' ≅ BZ
XY || X'Y'
Answers
GPT-4o mini
Let's go through each question one by one:
### 1. Pre-image of F' after reflection
To find the pre-image of point F' after it was reflected across the line y = -x, we use the reflection rule for this line: (x, y) → (-y, -x).
Given the coordinates of F':
- F' = (4, -2)
Now applying the reflection rule:
- Pre-image point F: (y, x) → (-(-2), -4) = (2, -4)
Among the options:
- (2, –4) is the correct answer.
### 2. Reflection of vertex G across the line y = x
To reflect a point (x, y) across the line y = x, the coordinates change to (y, x).
For G:
- G = (4, -5)
Applying the reflection rule:
- G' = (-5, 4)
Among the options:
- (–5, 4) is the correct answer.
### 3. Rule for the reflection from the first triangle to the second triangle
Observe the points of the triangles. The points L, M, N are:
- M (-5, 4)
- N (-2, 3)
- L (-4, 2)
The reflected points are:
- L' (-4, -2)
- M' (-5, -4)
- N' (-2, -3)
It appears that the y-coordinates are negated while the x-coordinates remain the same. Thus, the reflection should occur across the x-axis.
The reflection rule is:
- rx-axis(x, y) → (x, -y)
Among the options:
- rx-axis(x, y) → (x, –y) is the correct answer.
### 4. Statements true for line of reflection EH between ΔABC and ΔA'B'C'
The properties of a line of reflection state that:
1. The midpoints of line segments connecting corresponding points of the pre-image and image should lie on the line of reflection.
2. The line of reflection is the perpendicular bisector of the segments connecting corresponding points.
Thus the correct statements are:
- BD = DB' (midpoint property)
- The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC' (perpendicular bisector property)
- DF = FG (midpoint property)
### 5. Statements true about the reflection of ΔXYZ across Line MN
For a correct reflection across a line, the following properties should hold:
1. Each midpoint of the segments connecting corresponding points lies on the line of reflection.
2. The segments connecting corresponding points are equal in length.
3. The segments from the points to the line of reflection must be equal.
Therefore, the true statements are:
- XX' ≅ YY' (equal length of segments)
- BZ' ≅ BZ (equal length from point to line)
- XY || X'Y' (the segments are parallel after reflection)
If any variables or descriptions are used for specifics, they assume clarity in context for a robust solution.
### 1. Pre-image of F' after reflection
To find the pre-image of point F' after it was reflected across the line y = -x, we use the reflection rule for this line: (x, y) → (-y, -x).
Given the coordinates of F':
- F' = (4, -2)
Now applying the reflection rule:
- Pre-image point F: (y, x) → (-(-2), -4) = (2, -4)
Among the options:
- (2, –4) is the correct answer.
### 2. Reflection of vertex G across the line y = x
To reflect a point (x, y) across the line y = x, the coordinates change to (y, x).
For G:
- G = (4, -5)
Applying the reflection rule:
- G' = (-5, 4)
Among the options:
- (–5, 4) is the correct answer.
### 3. Rule for the reflection from the first triangle to the second triangle
Observe the points of the triangles. The points L, M, N are:
- M (-5, 4)
- N (-2, 3)
- L (-4, 2)
The reflected points are:
- L' (-4, -2)
- M' (-5, -4)
- N' (-2, -3)
It appears that the y-coordinates are negated while the x-coordinates remain the same. Thus, the reflection should occur across the x-axis.
The reflection rule is:
- rx-axis(x, y) → (x, -y)
Among the options:
- rx-axis(x, y) → (x, –y) is the correct answer.
### 4. Statements true for line of reflection EH between ΔABC and ΔA'B'C'
The properties of a line of reflection state that:
1. The midpoints of line segments connecting corresponding points of the pre-image and image should lie on the line of reflection.
2. The line of reflection is the perpendicular bisector of the segments connecting corresponding points.
Thus the correct statements are:
- BD = DB' (midpoint property)
- The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC' (perpendicular bisector property)
- DF = FG (midpoint property)
### 5. Statements true about the reflection of ΔXYZ across Line MN
For a correct reflection across a line, the following properties should hold:
1. Each midpoint of the segments connecting corresponding points lies on the line of reflection.
2. The segments connecting corresponding points are equal in length.
3. The segments from the points to the line of reflection must be equal.
Therefore, the true statements are:
- XX' ≅ YY' (equal length of segments)
- BZ' ≅ BZ (equal length from point to line)
- XY || X'Y' (the segments are parallel after reflection)
If any variables or descriptions are used for specifics, they assume clarity in context for a robust solution.