Question

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 a triangle $\triangle ABC$ in the coordinate - plane. For example, let $A=(1,1)$, $B=(3,1)$, $C=(1,3)$.

Step2: Apply a rigid transformation

Let's apply a translation. Translate $\triangle ABC$ 2 units to the right and 3 units up. The translation rule is $(x,y)\to(x + 2,y + 3)$. So, $A'=(1+2,1 + 3)=(3,4)$, $B'=(3+2,1 + 3)=(5,4)$, $C'=(1+2,3 + 3)=(3,6)$.

Step3: Apply a dilation

Let's apply a dilation with a scale factor of 2 centered at the origin $(0,0)$. The dilation rule is $(x,y)\to(2x,2y)$. So, $A''=(2\times3,2\times4)=(6,8)$, $B''=(2\times5,2\times4)=(10,8)$, $C''=(2\times3,2\times6)=(6,12)$.

Step4: Draw the final triangle

Draw and label $\triangle A''B''C''$ in the coordinate - plane.

Answer:

Follow the above - described steps to draw $\triangle ABC$, $\triangle A'B'C'$ and $\triangle A''B''C''$ in the coordinate plane.