Question

the table shows the coordinates of the vertices of △abc and its △abc. △abc: a(0,0), b(10, - 20), c(-10, - 20); △abc: a(0,10), b(10, - 10), c(-10, - 10). which translation maps △abc to its image? 10 units down 10 units up 10 units to the right 10 units to the left

Explanation:

Step1: Analyze x - coordinates

The x - coordinates of corresponding vertices in $\triangle ABC$ and $\triangle A'B'C'$ are the same. For example, $x_A = 0,x_{A'}=0$; $x_B = 10,x_{B'}=10$; $x_C=- 10,x_{C'}=-10$.

Step2: Analyze y - coordinates

For vertex $A$, $y_A = 0,y_{A'}=10$; for vertex $B$, $y_B=-20,y_{B'}=-10$; for vertex $C$, $y_C=-20,y_{C'}=-10$. The change in y - coordinate for each vertex is $\Delta y=y_{new}-y_{old}=10$. A positive change in the y - coordinate means moving up.

Answer:

10 units up