Question

1. if ab = 20 and ac = 30, then find the value for bc. be sure to include your work. (2 pts)
2. b is the midpoint of line segment ac. if ab = x+2 and bc = 30, find the value of x. be sure to include your work.(3 pts)

Explanation:

Step1: Use segment - addition postulate for question 4

Since points A, B, and C are collinear and B lies between A and C, by the segment - addition postulate \(AC=AB + BC\). We know \(AB = 20\) and \(AC = 30\). Substitute the values into the formula: \(30=20 + BC\).

Step2: Solve for BC

Subtract 20 from both sides of the equation \(30=20 + BC\). So, \(BC=30 - 20=10\).

Step3: Use mid - point property for question 5

If B is the mid - point of line segment AC, then \(AB = BC\) by the definition of a mid - point. We know \(AB=x + 2\) and \(BC = 30\). So, \(x+2=30\).

Step4: Solve for x

Subtract 2 from both sides of the equation \(x + 2=30\). We get \(x=30 - 2=28\).

Answer:

1. \(BC = 10\)
2. \(x = 28\)