Question

1. find the distance from point a to point b. round your answer to the nearest tenth (first decimal place) if necessary.

Explanation:

Step1: Identify the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Assume the coordinates of point A are $(x_1,y_1)$ and of point B are $(x_2,y_2)$. From the grid - like structure, if we assume the grid has a unit length of 1, and count the horizontal and vertical displacements. Let's say the horizontal displacement $\Delta x=x_2 - x_1$ and the vertical displacement $\Delta y=y_2 - y_1$.

Step2: Determine the displacements

By counting the grid squares, assume the horizontal displacement $\Delta x$ and vertical displacement $\Delta y$. If we count the number of grid - squares from point A to point B horizontally and vertically, we find that the horizontal change (run) and vertical change (rise) form the two legs of a right - triangle. Suppose the horizontal distance between A and B is $a$ and the vertical distance is $b$. By counting, assume $a = 4$ and $b = 3$.

Step3: Apply the Pythagorean theorem (equivalent to distance formula for 2D)

The distance $d$ between A and B is given by $d=\sqrt{a^{2}+b^{2}}$. Substitute $a = 4$ and $b = 3$ into the formula: $d=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5$.

Answer:

5