Question

triangle abc is translated according to the rule (x, y) → (x + 2, y - 8). if the coordinates of the pre - image of point b are (4, - 5), what are the coordinates of b?
○ (2, 3)
○ (1, - 9)
○ (- 3, - 4)
○ (6, - 13)

Explanation:

Step1: Identify the translation rule

The translation rule is \((x, y) \to (x + 2, y - 8)\), where \((x, y)\) is the pre - image and \((x + 2, y - 8)\) is the image.

Step2: Substitute the pre - image coordinates

The pre - image of point \(B\) is \((4,-5)\). So we substitute \(x = 4\) and \(y=-5\) into the translation rule.
For the \(x\) - coordinate of the image: \(x_{new}=x + 2=4 + 2\)
For the \(y\) - coordinate of the image: \(y_{new}=y-8=-5 - 8\)

Step3: Calculate the new coordinates

Calculate \(x_{new}\): \(4 + 2=6\)
Calculate \(y_{new}\): \(-5-8=-13\)

Answer:

(6, -13)