Multiple Choice
Triangle STU below is translated right 2 units and 3 units down. What are the coordinates of the vertices of the image?
A coordinate grid with triangle S T U drawn on the grid is shown.The x-axis is between negative 12 and 4 with interval marks representing one unit, and the y-axis is between negative 4 and 14 with interval marks representing one unit. Triangle S T U is drawn in red with vertex S at left-parenthesis negative 6 comma 10 right-parenthesis, vertex T at left-parenthesis negative 9 comma 3 right-parenthesis, and vertex U at left-parenthesis negative 3 comma 3 right-parenthesis.
A. S’(−9, 12), T’(−12, 5), U’(−6, 5)
B. S’(−4, 7), T’(−7, 0), U’(−1, 0)
C. S’(−8, 13), T’(−11, 6), U’(−5, 6
D. S’(−4, 10), T’(−7, 3), U’(−1, 3)
A. S’(−9, 12), T’(−12, 5), U’(−6, 5)
What is the constant of proportionality for the relationship between the number of cups of flour and the number of batches of cookies?
A graph on a coordinate grid is shown.The x-axis is labeled 'Cups of Flour' and is between 0 and 18 with interval marks representing two units. The y-axis is labeled 'Batches of Cookies' and is between 0 and 8 with interval marks representing one unit. A line is drawn connecting the points:
· left-parenthesis 0 comma 0 right-parenthesis
· left-parenthesis 2 comma 1 right-parenthesis
· left-parenthesis 4 comma 2 right-parenthesis
· left-parenthesis 6 comma 3 right-parenthesis
· left-parenthesis 8 comma 4 right-parenthesis
· left-parenthesis 10 comma 5 right-parenthesis
· left-parenthesis 12 comma 6 right-parenthesis
· left-parenthesis 14 comma 7 right-parenthesis
· left-parenthesis 16 comma 8 right-parenthesis
A. 0.25
B. 0.5
C. 2
D. 4
B. 0.5
To determine the coordinates of the image after translating the triangle, you need to remember that a translation involves shifting the shape horizontally and vertically.
In this case, the triangle is translated 2 units to the right and 3 units down. To find the new coordinates, we can apply these shifts to the original coordinates of each vertex.
Starting with the original coordinates of the vertices:
S(-6, 10)
T(-9, 3)
U(-3, 3)
We can now apply the translations:
- Move 2 units to the right: Add 2 to the x-coordinates
- Move 3 units down: Subtract 3 from the y-coordinates
Applying these translations, we get the new coordinates:
S'(-6 + 2, 10 - 3) = S'(-4, 7)
T'(-9 + 2, 3 - 3) = T'(-7, 0)
U'(-3 + 2, 3 - 3) = U'(-1, 0)
So, the image coordinates of the vertices after the translation are:
S'(-4, 7)
T'(-7, 0)
U'(-1, 0)
Looking at the answer choices provided, we can see that option B matches the calculated coordinates:
S’(-4, 7), T’(-7, 0), U’(-1, 0)
Therefore, the correct answer is B.