Question

1. point a is plotted at (8, -2). use the graph to answer parts (a)-(c).

a. write the ordered pair of the reflection of point a across the x-axis.
b. write the ordered pair of the reflection of point a across the y-axis.
c. write the ordered pair of the reflection of point a across the x-axis and then across th

Explanation:

Part (a)

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is \((x,-y)\).

Step2: Apply the rule to point \(A(8,-2)\)

For point \(A(8,-2)\), \(x = 8\) and \(y=-2\). Using the rule \((x,-y)\), we substitute \(y = - 2\) into \(-y\), so \(-y=-(-2)=2\). So the reflected point is \((8,2)\).

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) across the \(y\) - axis is \((-x,y)\).

Step2: Apply the rule to point \(A(8,-2)\)

For point \(A(8,-2)\), \(x = 8\) and \(y = - 2\). Using the rule \((-x,y)\), we substitute \(x = 8\) into \(-x\), so \(-x=-8\). So the reflected point is \((-8,-2)\).

Step1: Reflect over x - axis first

From part (a), the reflection of \(A(8,-2)\) over the \(x\) - axis is \((8,2)\).

Step2: Reflect the new point over y - axis

Now we reflect the point \((8,2)\) over the \(y\) - axis. Using the rule for reflection over \(y\) - axis \((-x,y)\), where \(x = 8\) and \(y = 2\). Substituting \(x = 8\) into \(-x\), we get \(-x=-8\). So the reflected point is \((-8,2)\).

Answer:

\((8,2)\)

Part (b)