Question

what is the distance between the points shown on the coordinate plane below? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Identify coordinates

First, find the coordinates of the two points. The upper point is at \((-1, 3)\) (wait, looking at the grid: the vertical line is y-axis, horizontal x-axis. The upper dot: x is -1 (since it's 1 unit left of y-axis), y is 3 (3 units above x-axis). The lower dot is at \((0, -1)\) (on y-axis, x=0, y=-1). Wait, maybe better to check again. Wait, the grid: each square is 1 unit. Let's re-express:

Wait, the upper point: x-coordinate: let's see, from y-axis (x=0), moving left 1 unit: x=-1. y-coordinate: from x-axis (y=0), moving up 3 units: y=3. So \((-1, 3)\).

The lower point: on y-axis, so x=0, y=-1 (since it's 1 unit below x-axis). So \((0, -1)\).

Step2: Apply distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Substitute \(x_1 = -1\), \(y_1 = 3\), \(x_2 = 0\), \(y_2 = -1\):

\(d = \sqrt{(0 - (-1))^2 + (-1 - 3)^2}\)

Simplify inside the square root:

\(0 - (-1) = 1\), \(-1 - 3 = -4\)

So \(d = \sqrt{(1)^2 + (-4)^2} = \sqrt{1 + 16} = \sqrt{17}\)

Step3: Calculate and round

\(\sqrt{17} \approx 4.123\), round to nearest tenth: 4.1

Wait, wait, maybe I misread the coordinates. Let me check again. Wait, the upper point: looking at the grid, the x-axis: from -6 to 6, y-axis from -6 to 6. The upper dot: x is -1? Wait, no, maybe the upper point is at (-1, 3)? Wait, no, maybe the upper point is at (-1, 3) and the lower at (0, -1). Wait, or maybe the upper point is at (-1, 3) and the lower at (0, -1). Wait, let's re-express:

Wait, the lower point is at (0, -1) (on y-axis, x=0, y=-1). The upper point: x is -1 (1 unit left of y-axis), y is 3 (3 units above x-axis). So the horizontal distance (Δx) is \(0 - (-1) = 1\), vertical distance (Δy) is \(-1 - 3 = -4\), so squared distances: \(1^2 = 1\), \((-4)^2 = 16\), sum is 17, square root of 17 is approx 4.123, so to nearest tenth is 4.1.

Wait, but maybe the coordinates are different. Wait, maybe the upper point is at (-1, 3) and the lower at (0, -1). Let me confirm:

Looking at the grid: the upper dot is at x=-1 (since it's one square left of y-axis), y=3 (three squares above x-axis). The lower dot is at x=0 (on y-axis), y=-1 (one square below x-axis). So yes, coordinates are (-1, 3) and (0, -1).

So distance is \(\sqrt{(0 - (-1))^2 + (-1 - 3)^2} = \sqrt{1 + 16} = \sqrt{17} \approx 4.1\)

Answer:

4.1