Question

a line segment with endpoints at ( p(1,8) ) and ( q(5,-2) ) is reflected across the ( y )-axis and translated up 6 units. what are the coordinates of the image of point ( q )?
( \bigcirc ) a ( (-5,4) )
( \bigcirc ) b ( (-1,14) )
( \bigcirc ) c ( (5,8) )
( \bigcirc ) d ( (1,-2) )

Explanation:

Step1: Reflect point \( Q(5, - 2) \) across the \( y - axis \)

When a point \((x,y)\) is reflected across the \(y - axis\), the rule is \((x,y)\to(-x,y)\).
For point \(Q(5,-2)\), after reflection across the \(y - axis\), it becomes \(Q'(-5,-2)\).

Step2: Translate the reflected point \( Q'(-5,-2) \) up \(6\) units

When a point \((x,y)\) is translated up \(k\) units, the rule is \((x,y)\to(x,y + k)\).
Here \(k = 6\), so for point \(Q'(-5,-2)\), we have \(y=-2+6 = 4\).
The new point is \((-5,4)\).

Answer:

A. \((-5,4)\)