Question

points a, b, and c do not lie on the same line. if the distance from a to b is 4 units, and the distance from b to c is 5 units, then what is the largest possible integer distance between points a and c?

Explanation:

Step1: Apply the triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), \(a + b>c\), \(a + c>b\), and \(b + c>a\). In the case of three non - collinear points \(A\), \(B\), and \(C\), if we consider the lengths \(AB = 4\) and \(BC=5\), and let \(AC=x\), then \(x

Step2: Calculate the upper bound

Substitute \(AB = 4\) and \(BC = 5\) into the inequality \(x

Answer:

\(8\)