What is the image of point P (-2, 3, 5) after a reflection about the xy-plane?
a. P' (-2, -3, 5)
b. P' (2, 3, 5)
c. P' (2, -3, -5)
d. P' (-2, 3, -5)
#2: What is the image point R (4, -1, -3) under the translation T (x, y, z) → T' (x - 2, y + 1, z - 4)?
a. R' (6, -2, 1)
b. R' (2, 0, -1)
c. R' (-2, 1, -4)
d. R' (2, 0, -7)
#3: Point A (1, -3, 4) is reflecting about the xz-plane. What are the coordinates of that reflection?
a. A' (1, 3, 4)
b. A' (1, -3, -4)
c. A' (-1, -3, 4)
d. A' (-1, 3, -4)
#4: What is the image of point Q (3, 5, -4) after it is reflected about the yz-plane?
a. Q' (-3, 5, 4)
b. Q' (3, -5, -4)
c. Q' (-3, 5, -4)
d. Q' (3, 5, 4)
#5: What is the image of point M (-3, 0, 5) under the translation T (x, y, z) → T' (x + 5, y -1, z - 4)?
a. M' (-2, 1, -1)
b. M' (2, -1, 1)
c. M' (-2, -1, 1)
d. M' (2, -1, -1)
(-2,3-5)
#1 D
#2 nope
#3 nope
#4 C
#5 B
Clearly you need to review these basic transformations.
Reflection through the xy plane changes the sign of the z coordinate.
xz: change y
yz: change x
for translations, just add the indicated amounts to the coordinates.
I got 4/5 for that same test.
To find the image point after a reflection or translation, we can apply the given transformation rules to the coordinates of the original point. Let's go through each question step by step to determine the correct answer.
#1: The reflection about the xy-plane negates the z-coordinate of the point, while keeping the x and y coordinates the same. So, the image of point P (-2, 3, 5) after reflection about the xy-plane is P' (-2, 3, -5). None of the given options match exactly, so the correct answer is not provided.
#2: The translation rule T (x, y, z) → T' (x - 2, y + 1, z - 4) means that the image point will have each coordinate decreased by 2, 1, and 4 respectively. Applying this rule to point R (4, -1, -3), we get R' (4 - 2, -1 + 1, -3 - 4) = R' (2, 0, -7). The correct answer is not one of the given options.
#3: Reflecting a point about the xz-plane keeps the y-coordinate the same, while negating the x and z coordinates. So, the reflection of point A (1, -3, 4) about the xz-plane gives A' (-1, -3, -4). The correct answer is not one of the given options.
#4: The reflection about the yz-plane negates the x-coordinate of the point, while keeping the y and z coordinates the same. Therefore, the image of point Q (3, 5, -4) after reflection about the yz-plane is Q' (-3, 5, -4). The correct answer is not one of the given options.
#5: The translation rule T (x, y, z) → T' (x + 5, y - 1, z - 4) means that each coordinate of the image point will be increased by 5, decreased by 1, and decreased by 4 respectively. Applying this rule to point M (-3, 0, 5), we get M' (-3 + 5, 0 - 1, 5 - 4) = M' (2, -1, 1). Therefore, the correct answer is b. M' (2, -1, 1).
In summary, the correct answers are:
#1: None of the given options.
#2: None of the given options.
#3: None of the given options.
#4: None of the given options.
#5: b. M' (2, -1, 1).