Question

i. write the algebraic notation that describes the translation to create abc from abc.
ii. draw the map of translating point a to point a in the paper version of this test.
(x,y)→(x - 5,y + 4)
(x,y)→(x + 5,y - 4)
(x,y)→(x - 4,y + 5)
(x,y)→(x + 4,y - 5)
o b
o a
o c
o d

Explanation:

Step1: Analyze horizontal translation

To find the horizontal (x - direction) translation, compare the x - coordinates of a point and its image. Let's take point A. Suppose the coordinates of point A are \((x_1,y_1)\) and of point \(A'\) are \((x_2,y_2)\). Looking at the graph, if we assume \(A\) is at \((- 8,2)\) and \(A'\) is at \((-3,-2)\), the change in the x - coordinate \(\Delta x=x_2 - x_1=-3-(-8)=5\). A positive change in the x - coordinate means a right - ward shift.

Step2: Analyze vertical translation

To find the vertical (y - direction) translation, compare the y - coordinates of a point and its image. Using the same points \(A(-8,2)\) and \(A'(-3,-2)\), the change in the y - coordinate \(\Delta y=y_2 - y_1=-2 - 2=-4\). A negative change in the y - coordinate means a downward shift.

Step3: Determine the translation rule

The general rule for translation is \((x,y)\to(x +\Delta x,y+\Delta y)\). Substituting \(\Delta x = 5\) and \(\Delta y=-4\), we get \((x,y)\to(x + 5,y - 4)\)

Answer:

B. \((x,y)\to(x + 5,y - 4)\)