Question

the figure below is reflected over y - axis and then translated up 4 units. what are the coordinates of the image of point q after these transformations?

Explanation:

1. First, identify the original coordinates of point Q:

• By observing the graph, the original coordinates of point Q are \((- 8,-8)\).

1. Then, apply the reflection - over - the y - axis rule:

• The rule for reflecting a point \((x,y)\) over the y - axis is \((-x,y)\).
• For point Q\((-8,-8)\), after reflecting over the y - axis, the new x - coordinate is \(-(-8)=8\), and the y - coordinate remains the same. So the coordinates after reflection are \((8,-8)\).

1. Next, apply the translation - up rule:

• The rule for translating a point \((x,y)\) up by \(k\) units is \((x,y + k)\). Here \(k = 4\).
• For the point \((8,-8)\), after translating up 4 units, the x - coordinate remains \(8\), and the new y - coordinate is \(-8 + 4=-4\).

Step1: Determine original coordinates

The original coordinates of Q are \((-8,-8)\).

Step2: Reflect over y - axis

Use the rule \((x,y)\to(-x,y)\), getting \((8,-8)\).

Step3: Translate up 4 units

Use the rule \((x,y)\to(x,y + 4)\), getting \((8,-4)\).

Answer:

\((8,-4)\)