Question

rigid or not rigid transformations

1. △abc plotted at a(-4,2), b(-7,2) and c(-7,7), is to be translated according to the rule (x,y)→(x + 10,y - 8).

a) plot the image of △abc under this translation and label it △abc. state the new coordinates: a = ______ b = ____ c = ______
b) was length preserved during this translation? ________ describe how you made your decision.

Explanation:

Step1: Find new coordinates of A'

Apply the translation rule $(x,y)\to(x + 10,y - 8)$ to point $A(-4,2)$.
$x=-4,y = 2$, so $x'=-4+10 = 6$ and $y'=2-8=-6$. So $A'=(6,-6)$.

Step2: Find new coordinates of B'

Apply the rule to point $B(-7,2)$.
$x=-7,y = 2$, so $x'=-7 + 10=3$ and $y'=2-8=-6$. So $B'=(3,-6)$.

Step3: Find new coordinates of C'

Apply the rule to point $C(-7,7)$.
$x=-7,y = 7$, so $x'=-7+10 = 3$ and $y'=7-8=-1$. So $C'=(3,-1)$.

Step4: Determine if length is preserved

Translation is a rigid - motion. In a translation, every point of the original figure is moved the same distance and in the same direction. The distance between any two points in the original figure and the distance between their corresponding points in the translated figure are equal. So, length is preserved.

Answer:

a) $A'=(6,-6)$, $B'=(3,-6)$, $C'=(3,-1)$
b) Yes. Translation is a rigid - motion and moves every point the same distance and in the same direction, so distances (lengths) between points are preserved.