Question

1. luke is going to reflect point r(6, 10) over the y-axis. what are the coordinates for r’?
2. if jkl is rotated 180° clockwise, which describes the location of j’?

grid with points k and axes shown

Explanation:

Problem 7:

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is that the \(x\) - coordinate changes its sign and the \(y\) - coordinate remains the same. So, if we have a point \(R(x,y)=(6,10)\), after reflection over the \(y\) - axis, the new point \(R'\) will have coordinates \((-x,y)\).

Step2: Apply the rule to point \(R(6,10)\)

Substitute \(x = 6\) and \(y = 10\) into the reflection rule. The \(x\) - coordinate of \(R\) is \(6\), so the \(x\) - coordinate of \(R'\) is \(- 6\), and the \(y\) - coordinate remains \(10\). So, \(R'=(-6,10)\).

Answer:

\((-6,10)\)

Problem 9:

First, we need to know the coordinates of point \(J\) from the graph. Let's assume (from the graph's grid) that the original coordinates of \(J\) are \((x,y)\). The rule for a \(180^{\circ}\) clockwise (or counter - clockwise, since \(180^{\circ}\) rotation is the same in both directions) rotation about the origin is \((x,y)\to(-x,-y)\).

1. Identify the coordinates of \(J\):

• From the grid, let's say the original coordinates of \(J\) are \((- 2,-6)\) (we need to check the grid lines. If we assume the position of \(J\) from the graph, for example, if \(J\) is at \((-2,-6)\)).

1. Apply the \(180^{\circ}\) rotation rule:

• Using the rule \((x,y)\to(-x,-y)\), if \(x=-2\) and \(y = - 6\), then \(-x=2\) and \(-y = 6\). So the coordinates of \(J'\) after a \(180^{\circ}\) rotation are \((2,6)\). (Note: The actual coordinates of \(J\) should be determined from the graph. If the original \(J\) has coordinates \((a,b)\), then \(J'\) will have coordinates \((-a,-b)\).)

Since the graph is not fully clear about the exact position of \(J\), but the general rule for \(180^{\circ}\) rotation about the origin is \((x,y)\to(-x,-y)\). If we assume the original \(J\) is at \((-2,-6)\) (by looking at the grid), then \(J'\) is at \((2,6)\).