Question

1. △abc plotted at a(-4,2), b(-7,2) and c(-7,7), is to be reflected over the y - axis.

a) plot the image of △abc under this reflection and label it △abc. state the new coordinates: a= b= c=
b) was length preserved during this reflection? yes describe how you made your decision.
c) are reflections rigid transformations? explain.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the $y$-axis is $(-x,y)$.

Step2: Find new coordinates of A

For point $A(-4,2)$, applying the rule $(-x,y)$, we get $A'(4,2)$.

Step3: Find new coordinates of B

For point $B(-7,2)$, applying the rule $(-x,y)$, we get $B'(7,2)$.

Step4: Find new coordinates of C

For point $C(-7,7)$, applying the rule $(-x,y)$, we get $C'(7,7)$.

Step5: Answer for length preservation

Length is preserved in a reflection because a reflection is a rigid - transformation. In a rigid - transformation, the distance between any two points in the pre - image is the same as the distance between the corresponding two points in the image. We can use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to verify. For example, the distance between two points in $\triangle ABC$ and the distance between the corresponding two points in $\triangle A'B'C'$ will be equal.

Step6: Answer for rigid transformation

Reflections are rigid transformations. A rigid transformation is a transformation that preserves distance and angle measures. In a reflection, the pre - image and the image have the same size and shape, and the distance between any two points in the pre - image is equal to the distance between the corresponding two points in the image, and the angle measures are also preserved.

Answer:

a) $A'=(4,2)$, $B'=(7,2)$, $C'=(7,7)$
b) Yes. A reflection is a rigid - transformation which preserves distance between points.
c) Yes. Reflections preserve distance and angle measures.