Question

what are the coordinates of point a? write your answer as an integer or decimal to the nearest 0.5.

Explanation:

Step1: Determine the x - coordinate

To find the x - coordinate of point A, we look at the horizontal (x - axis) position. Each grid line represents an integer value. Point A is between \(x=-2\) and \(x = - 1\). Since we need to round to the nearest \(0.5\), the mid - point between \(-2\) and \(-1\) is \(-1.5\). Looking at the position of point A, it is closer to \(x=-2\) or \(x=-1.5\)? Wait, let's re - examine. The x - coordinate: Let's see the grid. The x - axis has marks at \(-5,-4,-3,-2,-1,0,1,2,3,4,5\). Point A is at a position where the x - value is \(-2\) plus a half - grid? Wait, no. Wait, the green dot for A: Let's count the units. From the origin (0,0), moving left (negative x - direction) 2 units and then a little? Wait, no, looking at the grid, the x - coordinate of A: Let's see the horizontal lines. The x - coordinate: Let's assume each grid square has a side length of 1 unit. The point A is at \(x=-2\) (since it's one unit left of \(x = - 1\))? Wait, no, the green dot for A is between \(x=-2\) and \(x=-1\), but more precisely, if we look at the x - axis, the x - coordinate of A: Let's check the horizontal position. The x - coordinate is \(-2\) (wait, no, the grid lines: the x - axis has ticks at integers. The point A is at \(x=-2\) (horizontal) and y - coordinate: let's check the vertical (y - axis) position.

Step2: Determine the y - coordinate

For the y - coordinate, we look at the vertical (y - axis) position. The y - axis has marks at \(5,4,3,2,1,0,-1,-2,-3,-4,-5\). Point A is below the x - axis (so y is negative). It is between \(y=-2\) and \(y=-1\). Rounding to the nearest \(0.5\), the mid - point between \(-2\) and \(-1\) is \(-1.5\). Wait, but looking at the position of point A, let's see: the green dot for A is at \(x=-2\) (wait, no, maybe \(x=-2\) is not correct. Wait, let's re - analyze the grid. Let's take the origin (0,0) as the center. The x - axis: moving left, the first tick is \(-1\), then \(-2\), etc. Wait, no, the x - axis ticks are at \(-5,-4,-3,-2,-1,0,1,2,3,4,5\). So the distance between two adjacent ticks (e.g., between \(-2\) and \(-1\)) is 1 unit. The point A: let's see its horizontal position. If we consider the x - coordinate, from the origin, moving left 2 units (to \(x = - 2\))? Wait, no, the green dot for A is at a position where the x - coordinate is \(-2\) (because it's one unit left of \(x=-1\))? Wait, maybe I made a mistake. Wait, the x - coordinate: let's count the number of units from the y - axis (x = 0). Point A is 2 units to the left of the y - axis, so \(x=-2\)? No, wait, the grid lines: between \(x=-2\) and \(x=-1\), the point A is closer to \(x=-2\) or \(x=-1.5\)? Wait, maybe the x - coordinate is \(-2\) and the y - coordinate: looking at the y - axis, the point A is between \(y=-2\) and \(y=-1\), and it's closer to \(y=-1.5\)? Wait, no, let's look at the graph again. The green dot for A: let's see the vertical position. The y - coordinate: the distance from the x - axis (y = 0) to the point A is 1.5 units below the x - axis? Wait, no, the y - axis has ticks at \(1,0,-1,-2\). So between \(y=-1\) and \(y=-2\), the mid - point is \(-1.5\). The point A is at \(x=-2\) (horizontal) and \(y=-1.5\) (vertical)? Wait, no, maybe the x - coordinate is \(-2\) (because it's 2 units left of the origin) and the y - coordinate is \(-1.5\) (because it's 1.5 units below the origin). Wait, let's confirm:

Looking at the grid, the x - coordinate of point A: each grid square is 1 unit. So moving left from the origin (x = 0) to x=-1, x=-2, etc. The point A is at x=-2 (since it's aligned with the x=-2 vertical line? Wait, no, the green dot is a bit to the right of x=-2? Wait, maybe I misread. Wait, the x - coordinate: let's see the horizontal axis. The ticks are at - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5. The point A is between x=-2 and x=-1, but closer to x=-2? Wait, no, maybe the x - coordinate is - 2 (exactly) and the y - coordinate is - 1.5. Wait, let's check the y - coordinate: the y - axis ticks are at 5,4,3,2,1,0,-1,-2,-3,-4,-5. The point A is between y=-1 and y=-2, and since we need to round to the nearest 0.5, the possible values are - 2, - 1.5, - 1. The point A is at a position that is 1.5 units below the x - axis (y=-1.5) and 2 units to the left of the y - axis (x=-2)? Wait, no, maybe x=-2 and y=-1.5.

Wait, let's re - express: In a coordinate plane, the coordinates of a point are given as \((x,y)\), where \(x\) is the horizontal (x - axis) value and \(y\) is the vertical (y - axis) value. For point A:

- To find \(x\): The point is 2 units to the left of the y - axis (since each grid line is 1 unit), so \(x=-2\) (wait, no, if the grid lines are at integers, then between \(x=-2\) and \(x=-1\), the mid - point is \(x=-1.5\). Wait, maybe the x - coordinate is \(-2\) (because it's on the vertical line of \(x=-2\))? Wait, the green dot for A: looking at the horizontal position, it's at \(x=-2\) (the vertical line passing through \(x=-2\)) and the vertical position: between \(y=-1\) and \(y=-2\), and since we need to round to the nearest 0.5, the y - coordinate is \(-1.5\). So the coordinates of point A are \((-2,-1.5)\).

Answer:

\((-2, - 1.5)\)