Question

the triangles on the grid below represent a translation.
to form the image, the pre-image moved

• five units right and three units up.
• two units right and three units up.
• five units left and three units down.

Explanation:

Identify corresponding vertices

The pre-image is triangle \(ABC\) and the image is triangle \(A'B'C'\).
Let's find the coordinates of corresponding vertices from the grid:

$$ B = (-4, -2) ightarrow B' = (1, 1) $$

Calculate horizontal and vertical shifts

Find the horizontal change (\(\Delta x\)) and vertical change (\(\Delta y\)):

$$ \Delta x = x_{B'} - x_B = 1 - (-4) = 5 $$

$$ \Delta y = y_{B'} - y_B = 1 - (-2) = 3 $$

Determine the translation direction

A positive horizontal change of \(5\) means a movement of \(5\) units right.
A positive vertical change of \(3\) means a movement of \(3\) units up.

Answer:

• five units right and three units up. (Correct answer)
• two units right and three units up.
• five units left and three units down.