Question

1. draw the translation of the triangle hot six units left and one unit down. label the image hot. is the image similar or congruent? how do you know?

Explanation:

Step1: Find the coordinates of original points

Assume \(H=(0,0)\), \(O=(3,4)\), \(T=(6,2)\)

Step2: Apply the translation rule \((x,y)\to(x - 6,y-1)\)

For \(H\): \((0-6,0 - 1)=(-6,-1)\)
For \(O\): \((3-6,4 - 1)=(-3,3)\)
For \(T\): \((6-6,2 - 1)=(0,1)\)

Step3: Plot the new points \(H'(-6,-1)\), \(O'(-3,3)\), \(T'(0,1)\) and connect them

Step4: Determine similarity or congruence

Translation is a rigid transformation. Rigid transformations preserve side - lengths and angles.

Answer:

The image \(H'O'T'\) is congruent to the triangle \(HOT\). Because translation is a rigid transformation that does not change the size and shape of the figure (preserves side - lengths and angles).