Question

the graph shows point a.
if point a is reflected across the x - axis, what are the coordinates of the new point?
options: (-3, 1), (3, 1), (-1, 3), (1, -3)

Explanation:

Step1: Identify coordinates of point A

From the graph, point A is at $(3, -1)$? Wait, no, looking at the grid: the x - coordinate (horizontal) and y - coordinate (vertical). Wait, the graph has point A at (3, -1)? Wait, no, the grid lines: let's check the axes. The x - axis (horizontal) and y - axis (vertical). Wait, the red dot A: looking at the grid, the x - coordinate (left - right) is 3 (since it's 3 units to the right of the origin on the x - axis? Wait, no, the y - axis is vertical. Wait, the coordinates of a point are (x, y), where x is horizontal (left - right, positive to the right) and y is vertical (up - down, positive up). So point A: looking at the grid, the x - coordinate is 3 (since it's in the column where x = 3) and the y - coordinate is - 1? Wait, no, the y - axis: the origin is (0,0). The point A is at (3, - 1)? Wait, no, the grid: let's see, the vertical lines (x - axis) and horizontal lines (y - axis). Wait, the red dot is at x = 3 (horizontal) and y=-1 (vertical)? Wait, no, maybe I got x and y reversed. Wait, the graph: the horizontal axis is y? No, no, standard coordinate system: horizontal is x - axis, vertical is y - axis. Wait, the labels: the horizontal axis has labels 5,4,3,2,1,0,-1,-2,-3,-4,-5 (left - right), and vertical axis has labels 5,4,3,2,1,0,-1,-2,-3,-4,-5 (up - down). Wait, point A is at (x, y) where x is the horizontal coordinate (left - right) and y is vertical (up - down). Wait, the red dot A: looking at the grid, the horizontal position (x) is 3 (since it's 3 units to the right of the origin on the x - axis? No, wait, the vertical axis (y - axis) is the one with the numbers going up and down. Wait, maybe the axes are labeled differently. Wait, the problem says "reflected across the x - axis". The rule for reflecting a point $(x,y)$ across the x - axis is $(x, -y)$. So first, find the coordinates of point A. From the graph, point A: let's check the grid. The x - coordinate (horizontal, left - right) is 3, and the y - coordinate (vertical, up - down) is - 1? Wait, no, maybe I messed up. Wait, the vertical axis (y - axis) has positive values going up. So if the point is below the x - axis (y = 0), the y - coordinate is negative. Wait, the red dot A: looking at the grid, the horizontal line (y - axis) at y=-1? No, wait, the grid lines: each square is 1 unit. So point A is at (3, - 1)? Wait, no, maybe the coordinates are (3, - 1), and when we reflect across the x - axis, the rule is (x, y)→(x, -y). Wait, no, wait: reflecting across the x - axis changes the sign of the y - coordinate. So if the original point is (x, y), the reflected point is (x, -y). Wait, let's re - examine the graph. Wait, maybe the original point A is (3, - 1)? No, wait, the options include (3,1), (-3,1), (1,-3), (-1,3). Wait, maybe I got the coordinates wrong. Wait, maybe the point A is at (3, - 1)? No, that can't be. Wait, maybe the axes are swapped. Wait, the horizontal axis is y - axis and vertical is x - axis? No, standard is x horizontal, y vertical. Wait, the problem says "the graph shows point A". Let's look at the options. The options are (-3,1), (3,1), (1,-3), (-1,3). So when reflecting across the x - axis, the rule is (x,y)→(x, -y). So first, find the original coordinates of A. From the graph, point A: let's see, the x - coordinate (horizontal) is 3, y - coordinate (vertical) is - 1? No, that would give (3,1) when reflected (since - (-1)=1). Wait, no, if original is (3, - 1), reflection over x - axis is (3,1). But wait, maybe the original point is (3, - 1)? Wait, the grid: the red dot is at x = 3 (horizontal) and y=-1 (vertical). So reflecting across x - axis: (x,y)→(x, -y), so (3, - 1)→(3,1). Wait, but the options have (3,1) as one of them. Wait, maybe I made a mistake in the original coordinates. Wait, maybe the original point A is (3, - 1), so reflecting over x - axis (which is the horizontal axis) changes the y - coordinate's sign. So (3, - 1) reflected over x - axis is (3, 1).

Step2: Apply reflection rule

The rule for reflecting a point $(x,y)$ across the x - axis is $(x,y)\to(x, -y)$. So if we find the coordinates of point A, then apply this rule. From the graph, point A has coordinates $(3, - 1)$ (assuming x is horizontal, y is vertical). Then reflecting across the x - axis, we keep the x - coordinate the same and change the sign of the y - coordinate. So $x = 3$, $y=-1$, so the new y - coordinate is $-(-1)=1$. So the new point is $(3,1)$.

Answer:

(3, 1) (the option labeled as (3, 1))