Question

find the distance between the points (4, 2.3) and (4, -6.9).

Explanation:

Step1: Identify the coordinates

The two points have the same \(x\)-coordinate (\(x = 4\)). So we can use the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(x_1=x_2\), which is \(d=\vert y_1 - y_2\vert\). Here \(y_1 = 2.3\) and \(y_2=-6.9\).

Step2: Calculate the distance

Substitute the values into the formula: \(d=\vert2.3-(-6.9)\vert=\vert2.3 + 6.9\vert\).
\(2.3+6.9 = 9.2\), and \(\vert9.2\vert=9.2\).

Answer:

\(9.2\)