Question

1. what is the vertical distance between points a and b on the coordinate plane shown? ______units

Explanation:

Step1: Identify y - coordinates of A and B

Let's assume each grid square has a side length of 1 unit. From the coordinate plane, point A is at a certain y - coordinate and point B is at another. Let's say the y - coordinate of A is \(y_A\) and of B is \(y_B\). By looking at the grid, if we consider the origin \(O(0,0)\), suppose point A is at \(y = 4\) (above the x - axis) and point B is at \(y=-2\) (below the x - axis).

Step2: Calculate vertical distance

The vertical distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) (when \(x_1 = x_2\), i.e., vertical line) is given by \(|y_1 - y_2|\). Here, since A and B are vertically aligned (same x - coordinate), if \(y_A=4\) and \(y_B = - 2\), then the vertical distance \(d=|4-(-2)|=|4 + 2|=6\). Alternatively, we can count the number of grid squares between A and B. From A to the x - axis, let's say there are 4 units, and from the x - axis to B, there are 2 units. So total vertical distance is \(4 + 2=6\) units.

Answer:

6