Question

1. rick is designing a series of icons for a new app. he has hired you to check some icons and to create some new ones. the icons will incorporate reflection, translation, and rotation.

use what you know about transformations to answer part a, part b and part c.
classify each transformation of \\( \triangle a b c \\) as a translation, rotation, or reflection. if a reflection, identify the line of reflection. if a rotation, describe the point and degree of rotation.

Explanation:

Part A

Step1: Analyze the transformation

We know that a translation is a slide of a figure. Looking at the coordinates of the vertices of \(\triangle ABC\) and \(\triangle A'B'C'\), we can observe that each point \((x,y)\) of \(\triangle ABC\) is transformed to \((x + 6,y)\). For example, if \(B(- 3,1)\) and \(B'(3,1)\), \(x\) - coordinate changes as \(-3+6 = 3\) and \(y\) - coordinate remains the same.

Part B

Step1: Analyze the transformation

A rotation of \(180^{\circ}\) clockwise about the origin \((0,0)\) has the rule \((x,y)\to(-x,-y)\). Let's check the vertices. Suppose \(A(-4,5)\), after \(180^{\circ}\) clockwise rotation about \((0,0)\), the new point \(A'(4, - 5)\). Also, if \(B(-3,1)\), then \(B'(3,-1)\) and if \(C(-1,1)\), then \(C'(1,-1)\)

Part C

Step1: Analyze the transformation

A reflection across the line \(y = 1\) has the rule \((x,y)\to(x,2 - y)\). Let's check for a point. Suppose \(C(-1,1)\), after reflection across \(y = 1\), \(C'(-1,1)\) (since \(2-1 = 1\)). For \(A(-4,5)\), \(2 - 5=-3\), so \(A'(-4,-3)\)

Answer:

Part A: d. Translation
Part B: a. \(180^{0}\) clockwise rotation about \((0,0)\)
Part C: e. Reflection on line \(y = 1\)