Question

The coordinate grid below shows triangle ABC and its image after translation, triangle A'B'C': Triangles ABC and A prime, B prime, C prime are shown. A is located at negative 6, 2. B is located at negative 5, 5. C is locat Which of the following completes the rule for this translation, (x, y) → (x + 6, ___)? (5 points)

y − 6 y + 6 y − 8 y + 8

Answer 1

The rule of translation (x,y) → (x+6 , y-8)

Explanation:

The rest of the question is the coordinates of the ΔABC and ΔA'B'C'

The coordinates of the ΔABC: A(-6,2) , B(-5,5) , C(-1,3)

The coordinates of the ΔA'B'C': A'(0,-6) , B'(1,-3) , C'(5,-5)

It is required the rule of translation.

By Comparing between any of the points and its image

For example between A and A'

Let A(-6,2) = (x,y) and A'(0,-6) = (x+h , y+k)

So, x = -6 and y = 2

And x+h = 0 , y+k = -6

Substitute with x and y to find h and k

So, -6 + h = 0 ⇒ h = 6

And 2 + k = -6 ⇒ k = -8

So, the rule of translation (x,y) → (x+6 , y-8)