Question

1. use the pythagorean theorem to find the distance between the two points. round your answer to the nearest tenth.

Explanation:

Step1: Identify horizontal and vertical distances

Let the two - dimensional points be \((x_1,y_1)\) and \((x_2,y_2)\). First, find the horizontal distance \(a=\vert x_2 - x_1\vert\) and the vertical distance \(b=\vert y_2 - y_1\vert\) between the two points.

Step2: Apply the Pythagorean theorem

The distance \(d\) between two points in a plane is given by the formula \(d=\sqrt{a^{2}+b^{2}}\) according to the Pythagorean theorem.

Step3: Calculate and round

After substituting the values of \(a\) and \(b\) into the formula, calculate the value of \(d\) and round it to the nearest tenth.

Since the points are not clearly labeled with coordinates in the image, assume for a general case. Let the horizontal displacement be \(a\) and vertical displacement be \(b\). For example, if \(a = 3\) and \(b=4\), then \(d=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\).

If we consider the points in a coordinate - grid system and find the actual \(a\) and \(b\) values for the given points:
Suppose the two points have coordinates \((x_1,y_1)\) and \((x_2,y_2)\) such that \(a=\vert x_2 - x_1\vert\) and \(b=\vert y_2 - y_1\vert\). Let's say \(a = 6\) and \(b = 8\), then \(d=\sqrt{6^{2}+8^{2}}=\sqrt{36+64}=\sqrt{100}=10\).

Answer:

The process to find the distance between two points using the Pythagorean theorem is as above. You need to determine the horizontal and vertical displacements \(a\) and \(b\) from the grid for the specific points and then calculate \(d=\sqrt{a^{2}+b^{2}}\) and round to the nearest tenth. Without specific coordinates from the grid, a numerical answer cannot be given. If you provide the coordinates of the two points (e.g., \((x_1,y_1)\) and \((x_2,y_2)\)), a more specific answer can be calculated.