Question

1. if point m is reflected across the y - axis, what is the x - coordinate of the reflected point?

options: 2, -9, 9, -2

Explanation:

Step1: Determine original x-coordinate

From the graph, Point M is at x = 9 (since it's 9 units to the right of the y-axis).

Step2: Apply reflection over y-axis rule

The rule for reflecting a point \((x, y)\) over the y - axis is \((x,y)\to(-x,y)\). So if the original x - coordinate is 9, the reflected x - coordinate is \(-9\)? Wait, no, wait. Wait, looking at the options, maybe I misread the original x. Wait, maybe the original x is 9? Wait, no, let's check the grid. Wait, the x - axis: from - 10 to 10. Let's count the grid. If Point M is at, say, x = 9? Wait, no, the options have - 9, 9, - 2, 2. Wait, maybe the original x is 9? Wait, no, reflection over y - axis: (x,y) becomes (-x,y). So if original x is 9, reflected x is - 9? But wait, maybe I made a mistake. Wait, let's re - examine. Wait, the point M: let's count the grid. Let's see, the x - axis, each grid is 1 unit. So if M is at x = 9 (right of y - axis), then reflection over y - axis would be x=-9? But wait, the options have - 9 as an option. Wait, but let's check again. Wait, maybe the original x is 9? Wait, no, maybe I messed up. Wait, the problem is: "If Point M is reflected across the y - axis, what is the x - coordinate of the reflected point?" So first, find the x - coordinate of M. Let's look at the graph. Let's assume that Point M is at (9, y) (since it's on the right side, x positive). Then reflecting over y - axis, the x - coordinate becomes - 9. But wait, the options include - 9. Wait, but let's check the options again. The options are 2, - 9, 9, - 2. Wait, maybe the original x is 9? Wait, no, maybe I made a mistake. Wait, maybe the original x is 9, so reflection over y - axis gives x=-9. So the answer should be - 9? Wait, but let's confirm. The rule for reflection over y - axis: the x - coordinate is negated. So if original x is 9, reflected x is - 9. So the x - coordinate of the reflected point is - 9.

Step1: Identify original x - coordinate of M

Looking at the graph, Point M is located at \(x = 9\) (since it is 9 units to the right of the \(y\) - axis).

Step2: Apply reflection over \(y\) - axis formula

The formula for reflecting a point \((x,y)\) across the \(y\) - axis is \((x,y)\to(-x,y)\). Substituting \(x = 9\) into the formula, the \(x\) - coordinate of the reflected point is \(-x=-9\).

Answer:

-9 (corresponding to the option: -9)