Question

△abc has vertices a(8, 0), b(5, -2), and c(3, 6). find the vertices of abc after the following translation. a (__) 3 b () 4 c (__) 5 4. write the ordered pair for the translated point b. type a response

Explanation:

Step1: Identify the translation rule

Assuming the translation is the same for all points (since it's a translation of the triangle). Wait, but the original problem's translation details are a bit unclear from the image, but looking at the first part where A', B', C' have some numbers (3,4,5? Maybe the translation vector is, say, if we assume the translation is, for example, if we look at the original points: A(8, 0), B(5, -2), C(1, 6). Wait, maybe the translation is (x - 5, y + 6)? No, wait, maybe the translation is given by the numbers 3,4,5? Wait, maybe the translation is (x - a, y + b) where a and b are such that when we translate A(8,0), we get A' with some value. Wait, maybe the translation is (x - 5, y + 6)? Wait, no, let's check the original B point: B is (5, -2). If we assume the translation is, for example, (x - 2, y + 6)? Wait, maybe the translation is (x - 5, y + 6)? Wait, no, maybe the translation is (x - 5, y + 6) is not right. Wait, maybe the translation is (x - 5, y + 6) for A: 8 - 5 = 3, 0 + 6 = 6? But the first number for A' is 3. Oh! Wait, maybe the translation is (x - 5, y + 6). Let's check A(8,0): 8 - 5 = 3, 0 + 6 = 6. So A' would be (3,6). Then B(5,-2): 5 - 5 = 0, -2 + 6 = 4. So B' would be (0,4). Wait, but the second number for B' is 4. Oh! That matches. So the translation is (x - 5, y + 6). Let's verify:

For point B(5, -2):

Step2: Apply translation to B

x-coordinate: 5 - 5 = 0

y-coordinate: -2 + 6 = 4

So B' is (0, 4)

Answer:

(0, 4)