Question

point h is located at coordinates (3,-4).

Explanation:

Step1: Identify the coordinate system

In a standard Cartesian coordinate system, the x - axis is horizontal and the y - axis is vertical. The coordinates of a point are given in the form \((x,y)\), where \(x\) is the horizontal (left - right) coordinate and \(y\) is the vertical (up - down) coordinate.

Step2: Analyze the position of point H

To find the coordinates of point H, we count the number of units it is from the origin (the intersection of the x - axis and y - axis) along the x - axis and y - axis.
- For the x - coordinate: Moving from the origin towards the left (negative x - direction) or right (positive x - direction). Point H is 3 units to the left of the origin, so the x - coordinate is \(- 3\) (wait, there is a mistake in the original problem statement? Wait, looking at the graph, the x - axis is labeled with the arrow downwards? Wait, no, maybe the axes are labeled differently. Wait, in the graph, the x - axis (the horizontal axis) has the arrow pointing down? No, that's non - standard. Wait, maybe it's a typo in the axis labels. Wait, in a standard graph, the x - axis is horizontal (left - right) and y - axis is vertical (up - down). But in the given graph, the vertical axis is labeled x (arrow down) and horizontal axis is labeled y (arrow right). So we need to adjust. So if the vertical axis is x (so moving up and down is x - direction) and horizontal axis is y (moving left and right is y - direction). Wait, the problem says "Point H is located at coordinates (3, - 4)". Wait, let's re - evaluate.
Wait, maybe the axes are mislabeled. Let's assume that the horizontal axis is the x - axis (even if labeled y) and vertical axis is y - axis (even if labeled x). Wait, no, the problem statement says "Point H is located at coordinates (3, - 4)". Let's check the graph. Point H is in the lower left. Let's count the units:
- If we consider the horizontal direction (let's say y - axis as per the label) and vertical direction (x - axis as per the label). Wait, this is confusing. Wait, the standard coordinate system: \((x,y)\) where \(x\) is the abscissa (horizontal) and \(y\) is the ordinate (vertical). But in the given graph, the vertical axis is labeled \(x\) (arrow down) and horizontal axis is labeled \(y\) (arrow right). So to get the coordinates \((x,y)\), \(x\) is the vertical coordinate and \(y\) is the horizontal coordinate.
- For the x - coordinate (vertical): Moving from the origin (intersection of x and y axes) downwards (since the arrow is down) is positive? Wait, no, in standard, up is positive y, right is positive x. But here, vertical axis is x (arrow down), horizontal is y (arrow right). So if we move down along x - axis, that's positive x, and right along y - axis is positive y.
- Point H: Let's count the vertical (x) units: from the origin, moving down 3 units? Wait, no, the problem says the coordinates are (3, - 4). Wait, maybe the axes are labeled correctly in the problem statement's text, and the graph has a label error. Let's go with the problem statement: "Point H is located at coordinates (3, - 4)". Wait, maybe the x - axis is horizontal (left - right) with positive to the right, and y - axis vertical (up - down) with positive up. Then a point with x = 3 and y=-4 would be 3 units to the right and 4 units down. But in the graph, point H is to the left and down. So there is a mistake in the problem statement or the graph. Wait, maybe the coordinates are (- 3, - 4)? Wait, no, the problem says (3, - 4). Wait, perhaps the x - axis is the vertical axis (labeled x) with positive down, and y - axis is horizontal (labeled y) with positive right. Then:
- x - coordinate: moving down 3 units from the origin, so x = 3.
- y - coordinate: moving left 4 units from the origin, so y=-4. Which matches the point H's position (left and down). So the coordinates of point H are (3, - 4) as given.

Answer:

The coordinates of point H are \((3, - 4)\)