Question

1. the image point of a after a translation right 4 units and up 3 units is the point b(-1,8). determine the coordinates of the pre - image point a.
2. the image of the point (9,0) under a translation is (7,4). find the coordinates of the image of the point (0,8) under the same translation.
3. the image of the point (9, - 2) under a translation is (10,3). find the coordinates of the image of the point (-8,4) under the same translation.

Explanation:

8.

Step1: Reverse the x - translation

A translation right 4 units is reversed by subtracting 4 from the x - coordinate of the image point. Let the pre - image point \(A\) have coordinates \((x,y)\). Given the image point \(B(-1,8)\), the x - coordinate of \(A\) is \(x=-1 - 4=-5\).

Step2: Reverse the y - translation

A translation up 3 units is reversed by subtracting 3 from the y - coordinate of the image point. The y - coordinate of \(A\) is \(y = 8-3 = 5\).

Step1: Find the translation vector

The translation from \((9,0)\) to \((7,4)\): The change in the x - coordinate is \(\Delta x=7 - 9=-2\), and the change in the y - coordinate is \(\Delta y=4 - 0 = 4\).

Step2: Apply the translation to \((0,8)\)

For the point \((0,8)\), the new x - coordinate is \(x=0+\Delta x=0+( - 2)=-2\), and the new y - coordinate is \(y=8+\Delta y=8 + 4=12\).

Step1: Find the translation vector

The translation from \((9,-2)\) to \((10,3)\): The change in the x - coordinate is \(\Delta x=10 - 9 = 1\), and the change in the y - coordinate is \(\Delta y=3-( - 2)=5\).

Step2: Apply the translation to \((-8,4)\)

For the point \((-8,4)\), the new x - coordinate is \(x=-8+\Delta x=-8 + 1=-7\), and the new y - coordinate is \(y=4+\Delta y=4 + 5=9\).

Answer:

\((-5,5)\)

9.