Triangle EFG is rotated 90° clockwise about the origin to create triangle E'F'G'. Which statement is not true?
A.If (x, y) represents the coordinates of a vertex of triangle EFG, then (-x, -y) represents the coordinates of the corresponding vertex of triangle E'F'G'.
B.If (x, y) represents the coordinates of a vertex of triangle EFG, then (v, -x) represents the coordinates of the corresponding vertex of triangle E'F'G'.
C.Triangle E'F'G' is congruent to triangle EFG.
D.The angle measures of triangle E'F'G' are equal to the corresponding angle measures of triangle EFG.
The statement that is not true is B. If (x, y) represents the coordinates of a vertex of triangle EFG, then (v, -x) does not represent the coordinates of the corresponding vertex of triangle E'F'G'. The correct coordinates of the corresponding vertex of triangle E'F'G' would be (-y, x).
Which representation of a transformation on a coordinate grid does not preserve congruence?
A. (X,y) ~ (1/4x, 1/4y)
B.(x,y) → (-x,y)
C. (x,y) -* (x+6, y+1)
D. (x,y) → (-y, x)
The representation of a transformation that does not preserve congruence is option C. (x, y) → (x+6, y+1). This transformation involves shifting the points horizontally by 6 units and vertically by 1 unit. This will change the distances and angles between the points, therefore not preserving congruence.
Triangle PQR is translated 5 units left and 2 units up. Write a rule that describes this transformation.
Move the correct answer to each box. Not all answers will be used.
(X, y) ~(. , )
A. X + 2
B. X - 2
C.X + 5
D.X - 5
E.Y + 2
F.Y-2
G.Y+ 5
H.Y - 5
The rule that describes the translation of Triangle PQR 5 units left and 2 units up is:
(X, y) ~ (X - 5, Y + 2)
So the correct answer would be:
- Box 1: B. X - 5
- Box 2: E. Y + 2
If rectangle ABCD is dilated by a scale factor of 1.5 with a center of dilation at vertex A, how does the area of A'B'C'D' compare with the area of ABCD?
A. The area of A'B'C'D' is 3 times the area of ABCD.
B. The area of A'B'C'D' is 6 times the area of ABCD.
C. The area of A'B'C'D' is 1.5 times the area of ABCD.
D. The area of A'B'C'D' is 2.25 times the area of ABCD.
The correct answer is D. The area of A'B'C'D' is 2.25 times the area of ABCD.
When a rectangle is dilated by a scale factor of 1.5, the dimensions (length and width) of the rectangle are multiplied by 1.5. Since the area of a rectangle is equal to its length times its width, the area is also multiplied by the square of the scale factor. In this case, the scale factor is 1.5, so the area of A'B'C'D' will be 1.5^2 = 2.25 times the area of ABCD.
ASSESSMENT
Question Id: 605261
** Triangle MNO is dilated by a scale factor of to create triangle M'N'O'.
The perimeter of triangle MNO is x units.
What is the perimeter in units of triangle M'N'O'?
A. ( 7/8) 2x units
B. 1/8× units
C. 8/7× units
D.7/8x units
8
The correct answer is C. The perimeter of triangle M'N'O' is 8/7 times the perimeter of triangle MNO.
When a figure is dilated by a scale factor, all of its corresponding sides are multiplied by the scale factor. In this case, the scale factor is 8/7. Therefore, the perimeter of M'N'O' will be 8/7 times the perimeter of MNO.
The figure is rotated 270° clockwise with the origin as the center of rotation to create a new figure. Which rule describes this transformation?
A (x,y) ->(-y, x)
B (x,y) -> (-y, -x).
C (x, y) -> (x + 1, y - 2)
D (x, y) -> (x - 2, y + 1)
The rule that describes the transformation of rotating the figure 270° clockwise with the origin as the center of rotation is:
A. (x, y) -> (-y, x)
In this rule, the x-coordinate becomes the negative y-coordinate and the y-coordinate becomes the x-coordinate, reflecting the figure across the y-axis and swapping the values of the original coordinates.
* Based on the figure shown, which proportion equation is true?
A AC/BC = DE/AE
B AB/AD = BC/DE
C AC/AD = BC/DE
D DE/BC = DB/AD
Without the figure shown, it is not possible to determine which proportion equation is true. The specific lengths and relationships between the sides of the figure are necessary to make a determination.
Please provide the figure or additional information related to the lengths and relationships between the sides in order to accurately answer the question.
Based on the figure shown, which proportion equation is true?
A AC/BC = DE/AE
B AB/AD = BC/DE
C AC/AD = BC/DE
D DE/BC = DB/AD
Triangles and proportionality
Without a specific figure or information about the triangles and their relationships, it is not possible to determine which proportion equation is true. The specific lengths and relationships between the sides of the triangles are necessary to make a determination.
Please provide more information or details about the figure and the triangles to accurately answer the question.
What is the value of DE if AB = 6, AD = 8, and BC = 3?
3.5
4
4.5
5
To find the value of DE, we can use the proportion BC/DE = AB/AD. Plugging in the given values:
3/DE = 6/8
Cross-multiplying:
6DE = 3 * 8
Simplifying:
6DE = 24
Dividing both sides by 6:
DE = 4
Therefore, the value of DE is 4.
*× Translations, reflections and rotations preserve congruence. Dilations do not preserve congruence. Drag each transformation to the appropriate box.
A (x,y) → (-y, x)
B (x,y) → (x, -y)
C (x, y) -> (×+4, y-3)
D (x,y) → (3x, 3y)
E (x, y) -> (0.5x, 0.5y)
F (x,y) → (-X, -y)
G (x, y) → (y; -x)
H (x,y) → (-X,y)
Translations, reflections, and rotations preserve congruence. So, we can move A, B, F, and G to the appropriate box.
Translations:
C (x, y) -> (x+4, y-3)
Reflections:
F (x,y) → (-x, -y)
Rotations:
A (x,y) → (-y, x)
G (x, y) → (y, -x)
Dilations do not preserve congruence. So, E and H are not moved anywhere.
So the transformations that preserve congruence are:
- Translations: C
- Reflections: F
- Rotations: A, G