A civil engineer is drawing a plan for the location and length of a new underground sewer pipe on a coordinate grid. The pipe on the plan will run from point N(a, -2) to point P(1, b) on the coordinate grid. Which expression represents the shortest distance between N and P in units? *

Using the distance between two points, it is found that the expression that represents the shortest distance between N and P in units is:

Considering two points, and , the distance between them is given by:

In this problem, the points are N(a, -2) and P(1,b), hence, their distance is:

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Step-by-step explanation:

If the pipe on the plan runs from point N(a, -2) to point P(1, b), the expression that represents the shortest distance between N and P in units, is expressed using the formula;

D = √(x₂-x₁)²+(y₂-y₁)²

Given the coordinates  N(a, -2) and P(1, b);

x₁ = a, y₁ = -2, x₂ = 1 and y₂ = b

NP = √(1-a)²+(b+2)²

Hence the expression that represents the shortest distance between N and P in units is √(1-a)²+(b+2)² units

f(x) is the value of the function. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane.

step-by-step explanation:

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