Question

draw the image of △abc under the translation (x,y)→(x,y + 3).

Explanation:

Step1: Identify the vertices of △ABC

Let the coordinates of point A be $(x_A,y_A)$, B be $(x_B,y_B)$ and C be $(x_C,y_C)$. From the graph, assume $A(- 4,-3)$, $B(1,0)$, $C(-6,2)$.

Step2: Apply the translation rule

The translation rule is $(x,y)\to(x,y + 3)$.
For point A: $x_{A'}=x_A=-4$, $y_{A'}=y_A + 3=-3 + 3=0$, so $A'(-4,0)$.
For point B: $x_{B'}=x_B=1$, $y_{B'}=y_B + 3=0 + 3=3$, so $B'(1,3)$.
For point C: $x_{C'}=x_C=-6$, $y_{C'}=y_C + 3=2+3 = 5$, so $C'(-6,5)$.

Step3: Plot the new - triangle

Plot the points $A'(-4,0)$, $B'(1,3)$ and $C'(-6,5)$ on the same coordinate - grid and connect them to form the image of △ABC under the given translation.

Answer:

Plot the points $A'(-4,0)$, $B'(1,3)$ and $C'(-6,5)$ and connect them to get the translated triangle.