Question

graph the image of rectangle jklm after a reflection over the y-axis.

Explanation:

Step1: Find coordinates of original points

First, identify the coordinates of the vertices of rectangle \(JKLM\). From the graph:

• \(J\): \((3, 5)\) (wait, looking at the grid, let's check again. Wait, the x - axis: the grid lines. Let's see, \(J\) is at x = 3? Wait no, the x - coordinate for \(J\): the vertical lines. Wait, the original points: looking at the graph, \(J\) is at (3,5)? Wait no, let's check the grid. The x - axis has marks at - 10, - 8, - 6, - 4, - 2, 0, 2, 4, 6, 8, 10. The y - axis has marks at - 10, - 8, - 6, - 4, - 2, 0, 2, 4, 6, 8, 10. So \(J\) is at (3,5)? Wait no, the orange points: \(J\) is at (3,5)? Wait, no, looking at the graph, \(J\) is at (3,5)? Wait, the x - coordinate for \(J\): the column. Let's see, \(J\) is in the column where x = 3? Wait, no, the original \(J\) is at (3,5)? Wait, no, let's look again. The original rectangle: \(J\) is at (3,5)? Wait, \(M\) is at (3,9), \(L\) is at (6,9), \(K\) is at (6,5), \(J\) is at (3,5). Wait, yes, because from \(J\) to \(K\) is horizontal, \(J\) to \(M\) is vertical. So coordinates:
• \(J(3, 5)\)
• \(K(6, 5)\)
• \(L(6, 9)\)
• \(M(3, 9)\)

Step2: Apply reflection over y - axis rule

The rule for reflection over the \(y\) - axis is \((x,y)\to(-x,y)\). So we apply this to each vertex:

• For \(J(3, 5)\): After reflection, \(J'(-3, 5)\)
• For \(K(6, 5)\): After reflection, \(K'(-6, 5)\)
• For \(L(6, 9)\): After reflection, \(L'(-6, 9)\)
• For \(M(3, 9)\): After reflection, \(M'(-3, 9)\)

Step3: Plot the reflected points

Now, plot the points \(J'(-3, 5)\), \(K'(-6, 5)\), \(L'(-6, 9)\), \(M'(-3, 9)\) on the coordinate plane and connect them to form the reflected rectangle.

Answer:

The image of rectangle \(JKLM\) after reflection over the \(y\) - axis has vertices at \(J'(-3, 5)\), \(K'(-6, 5)\), \(L'(-6, 9)\), and \(M'(-3, 9)\). (To graph, plot these points and connect them in order.)