Question

there is a coordinate system with points (1,2) and (4,7) marked, and a blue arrow - like line segment between the vertical line at x = 1 (y = 2) and x = 4 (y = 2).

Explanation:

Step1: Identify the two points

We have two points \((1, 2)\) and \((4, 2)\).

Step2: Use the distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 1,y_1 = 2,x_2=4,y_2 = 2\). Since \(y_1=y_2 = 2\), the formula simplifies to \(d=\vert x_2 - x_1\vert\) (because the vertical distance is \(0\)).

Step3: Calculate the distance

Substitute the values: \(d=\vert4 - 1\vert=\vert3\vert = 3\).

Answer:

The distance between the two points \((1,2)\) and \((4,2)\) is \(3\).