The vertices of a rectangle are R(-5,-5), S(-1,-5), T(-1,1), and U(-5,1). After translation, R prime is the point (0,-13). Find the translation vector and coordinates of U prime.
I got (5,-8) as my translation vector and (0,-7) as U prime. Is this right?
To find the translation vector, we need to find the difference between the original point and its corresponding translated point. In this case, we have R(-5, -5) and R' (0, -13).
The translation vector (a, b) can be calculated as:
a = x-coordinate of R' - x-coordinate of R
= 0 - (-5)
= 5
b = y-coordinate of R' - y-coordinate of R
= -13 - (-5)
= -8
So, the translation vector is (5, -8).
Next, let's find the coordinates of U prime.
We know that U(-5, 1) is one of the vertices of the original rectangle. To find U prime, we need to apply the translation vector to U.
Adding the translation vector to the coordinates of U, we get:
U' = (x-coordinate of U + a, y-coordinate of U + b)
= (-5 + 5, 1 + (-8))
= (0, -7)
Therefore, the coordinates of U prime are (0, -7).
So, your translation vector (5, -8) is correct, but the coordinates of U prime should be (0, -7), not (0, -8).
To find the translation vector, you need to determine the difference between the coordinates of the pre-image point and the corresponding image point. In this case, you have the coordinates of R(-5, -5) and its image R' (0, -13). To find the translation vector, subtract the x-coordinates and the y-coordinates separately:
x-coordinate translation = x'-coordinate - x-coordinate = 0 - (-5) = 5
y-coordinate translation = y'-coordinate - y-coordinate = -13 - (-5) = -8
So, the translation vector is (5, -8).
To find the coordinates of U prime, you need to apply the same translation vector to the coordinates of U(-5, 1). Add the x-coordinate translation (5) to the x-coordinate of U and add the y-coordinate translation (-8) to the y-coordinate of U:
x-coordinate of U' = x-coordinate of U + x-coordinate translation = -5 + 5 = 0
y-coordinate of U' = y-coordinate of U + y-coordinate translation = 1 - 8 = -7
Therefore, the coordinates of U prime are (0, -7), which matches your answer. Well done!