Question

point d is located at the coordinates (2, 3). point d is translated 6 units left, reflected across the y-axis, and translated 6 units up to create its image, d. what are the coordinates of d? enter the coordinates for the translated point, d, as (x, y). d =

Explanation:

Step1: Translate 6 units left

To translate a point \((x, y)\) \(a\) units left, we subtract \(a\) from the \(x\)-coordinate. Given \(D(2, 3)\) and translating 6 units left, the new \(x\)-coordinate is \(2 - 6=-4\), and the \(y\)-coordinate remains \(3\). So the point after translation is \((-4, 3)\).

Step2: Reflect across the y - axis

The rule for reflecting a point \((x, y)\) across the \(y\)-axis is \((x,y)\to(-x,y)\). For the point \((-4, 3)\), after reflection across the \(y\)-axis, the \(x\)-coordinate becomes \(-(-4) = 4\), and the \(y\)-coordinate remains \(3\). So the point after reflection is \((4, 3)\).

Step3: Translate 6 units up

To translate a point \((x, y)\) \(b\) units up, we add \(b\) to the \(y\)-coordinate. For the point \((4, 3)\) and translating 6 units up, the new \(y\)-coordinate is \(3+6 = 9\), and the \(x\)-coordinate remains \(4\). So the final point \(D'\) has coordinates \((4, 9)\).

Answer:

\((4, 9)\)