Question

8 math journal draw a triangle in the coordinate plane and label it △abc. transform △abc using one rigid transformation and one dilation. draw and label the final image △abc.

Explanation:

Step1: Draw the initial triangle

Draw $\triangle ABC$ with vertices $A(1,1)$, $B(3,1)$, $C(1,3)$ on the coordinate - plane.

Step2: Apply a rigid transformation

Let's apply a translation. Translate $\triangle ABC$ 2 units to the right and 1 unit up. The new vertices $A'(1 + 2,1+1)=A'(3,2)$, $B'(3 + 2,1 + 1)=B'(5,2)$, $C'(1+2,3 + 1)=C'(3,4)$. So we have $\triangle A'B'C'$.

Step3: Apply a dilation

Let the center of dilation be the origin $(0,0)$ and the scale factor $k = 2$. For a point $(x,y)$ dilated about the origin with scale factor $k$, the new point is $(kx,ky)$. For $A'(3,2)$, $A''=2\times(3,2)=(6,4)$. For $B'(5,2)$, $B''=2\times(5,2)=(10,4)$. For $C'(3,4)$, $C''=2\times(3,4)=(6,8)$. Then draw and label $\triangle A''B''C''$.

Answer:

The steps above show how to draw $\triangle ABC$, perform a rigid - transformation (translation) and a dilation to get $\triangle A''B''C''$. You need to actually draw these on the given coordinate - plane with proper labels.