Question

an environmental engineer graphed the locations of a well and all of the drainage ditches in the vicinity. she positioned the well at (-8,7) and the farthest drainage ditch at (61,7). if each unit on the graph represents 1 foot, then how far away from the well is the farthest drainage ditch? ft

Explanation:

Step1: Identify the formula for distance on a coordinate plane (same y - coordinate)

When two points \((x_1,y_1)\) and \((x_2,y_2)\) have the same \(y\) - coordinate (\(y_1 = y_2\)), the distance \(d\) between them is given by \(d=\vert x_2 - x_1\vert\). Here, \(x_1=-8\), \(x_2 = 61\), and \(y_1=y_2 = 7\).

Step2: Calculate the absolute difference of the x - coordinates

Substitute the values of \(x_1\) and \(x_2\) into the formula: \(d=\vert61-(-8)\vert\). Using the rule \(a-(-b)=a + b\), we get \(d=\vert61 + 8\vert\).

Step3: Simplify the absolute - value expression

\(\vert61+8\vert=\vert69\vert=69\)

Answer:

\(69\)