Question

Triangle XYZ, with vertices X(-2, 0), Y(-2, -1), and Z(-5, -2), undergoes a transformation to form triangle X′Y′Z′, with vertices X′(4, -2), Y′(4, -3), and Z′(1, -4). The type of transformation that triangle XYZ undergoes is a_____ .
Triangle X′Y′Z′ then undergoes a transformation to form triangle X′Y′Z′, with vertices X″(4, 2), Y″(4, 3), and Z″(1, 4). The type of transformation that triangle X′Y′Z′ undergoes is a _____

Answer 1

Answer with explanation:

1)

The vertices of X,Y and Z are:

X(-2, 0), Y(-2, -1), and Z(-5, -2)

Now, when X,Y and Z are translated by using the translation transformation:

         (x,y) → (x+6,y-2)

Then we obtain the transformation:    

X(-2, 0) → X′(4, -2)

Y(-2, -1) → Y′(4, -3)

Z(-5, -2) →  Z′(1, -4)

The type of transformation that triangle XYZ undergoes is a translation transformation by the rule:   (x,y) → (x+6,y-2)

2)

Next when we reflect the triangle X'Y'Z' across the x-axis then we obtain X"Y"Z"

Since, the rule that follow on reflecting across x-axis is:

           (x,y) → (x,-y)

Hence, we get:

X′(4, -2) → X″(4, 2)

Y′(4, -3) →  Y″(4, 3)

Z′(1, -4) → Z″(1, 4)

Hence, the type of transformation that triangle X′Y′Z′ undergoes is a reflection transformation (on reflecting across x-axis)