Question

find the distance between the points (-4.6, 4.7) and (7.7, 4.7).

Explanation:

Step1: Identify the formula for distance between two points with same y - coordinate

Since the \(y\) - coordinates of the two points \((-4.6,4.7)\) and \((7.7,4.7)\) are the same (\(y_1 = y_2=4.7\)), the distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d=\vert x_2 - x_1\vert\).

Step2: Substitute the values of \(x_1\) and \(x_2\)

Here \(x_1=-4.6\) and \(x_2 = 7.7\). Then \(d=\vert7.7-(-4.6)\vert\).
Using the rule \(a-(-b)=a + b\), we have \(d=\vert7.7 + 4.6\vert\).

Step3: Calculate the absolute value

\(7.7+4.6 = 12.3\), and \(\vert12.3\vert=12.3\).

Answer:

\(12.3\)