Question

1. what is the result of applying a translation of (3,4) followed by a translation of (-3,-4)?

reflected coordinates
moved coordinates
original coordinates
rotated coordinates

• required

3

Explanation:

Step1: Understand translation rules

Translation is a transformation that moves every point of a figure or space by the same distance in a given direction. If we have a translation vector \((a,b)\), the rule for translating a point \((x,y)\) is \((x',y')=(x + a,y + b)\).

Step2: Apply the first translation

First, we apply the translation \((3,4)\). Let the original coordinates be \((x,y)\). After the first translation, the coordinates become \((x_1,y_1)=(x + 3,y + 4)\).

Step3: Apply the second translation

Then we apply the translation \((- 3,-4)\) to the point \((x_1,y_1)\). Using the translation rule \((x_2,y_2)=(x_1-3,y_1 - 4)\). Substitute \(x_1=x + 3\) and \(y_1=y + 4\) into the second - translation formula: \(x_2=(x + 3)-3=x\) and \(y_2=(y + 4)-4=y\).

Answer:

Original coordinates